Question 12 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A heart.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
A heart: There are $14$ cards of heart
$\therefore m = 13$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{13}{52}=\frac{1}{4}$
View full question & answer→Question 22 Marks
A box contains $20$ cards numbered from $1$ to $20$. A card is drawn at random from the box. Find the probability that the number on the drawn card is:
- Divisible by $2$ or $3.$
- A prime number.
AnswerTotal number of outcomes $= 20$
- The numbers from $1$ to $20$ which are divisible by $2$ or $3$ are $2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18$ and $20.$
So, the favourable number of outcomes are $13.$
$\therefore P($number on the drawn card is divisible by $2$ or $3)$
$=\frac{\text{Favourable number of outcomes}}{\text{Total number of outcomes}}=\frac{13}{20}$
- The prime numbers from $1$ to $20$ are $2, 3, 5, 7, 11, 13, 17$ and $19$.
So, the favourable number of outcomes are $8.$
$\therefore P($number on the drawn card is a prime number$)$
$=\frac{\text{Favourable number of outcomes}}{\text{Total number of outcomes}}$
$=\frac{8}{20}=\frac{2}{5}$ View full question & answer→Question 32 Marks
A number is selected at random from first $50$ natural numbers. Find the probability that it is a multiple of $3$ and $4.$
AnswerTotal number of natural numbers $= 50$
Numbers which are divisible by $3$ and $4$
$= 12, 24, 36, 48 = 4$ numbers
$\therefore\ \text{Probability P}_\text{(E)}=\frac{4}{50}=\frac{2}{25}$
View full question & answer→Question 42 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Jack.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Jack : There are $4$ jacks
$\therefore m = 4$
$\therefore\ \text{P(A)}=\frac{4}{52}=\frac{1}{13}$
View full question & answer→Question 52 Marks
Examine each of the following statements and comment:
If a die in thrown once, there are two possible outcomes $-$ an odd number or an even number. Therefore, the probability of obtaining an odd number is $\frac{1}{2}$ and the probability of obtaining an even number is $\frac{1}{2}$.
AnswerCorrect.
When a dice is thrown, the possible outcomes are $1, 2, 3, 4, 5,$ and $6.$ Out of these $1, 3, 5$ are odd and $2, 4, 6$ are even numbers.
Therefore, the probability of getting an odd number is $\frac{1}{2}$.
Similarly, the probability of getting an even number is $\frac{1}{2}$.
View full question & answer→Question 62 Marks
A bag contains $3$ red and $5$ black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red$?$
AnswerNumber of red balls $= 3$
Number of black balls $= 5$
Total number of balls $= 3 + 5 = 8$ balls
No. of favourable outcomes $= 5$
$\therefore\ \text{Probability}=\frac{5}{8}$
View full question & answer→Question 72 Marks
Tickets numbered from $1$ to $20$ are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of $3$ or $7?$
AnswerNo. of tickets bearing numbers from $1$ to $20 = 20$
Numbers which are multiple of $3$ of $7$ can be $3, 6, 7, 96, 12, 14, 15, 18 =$ which are $8$
$\therefore m = 8$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{8}{20}=\frac{2}{5}$
View full question & answer→Question 82 Marks
A die is thrown once. What is the probability of getting a number greater than $4?$
AnswerNumbers greater then $4$ on the dice are $5$ and $6$
$\therefore\ \text{P(E)}=\frac{\text{m}}{\text{n}}=\frac{2}{6}=\frac{1}{3}$
View full question & answer→Question 92 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Neither a king nor a queen.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Neither a king nor a queen
Number of favourable outcomes
$= 52 - (4 + 4)$
$= 52 - 8 = 44$
$\therefore\ \text{Probability}=\frac{44}{52}=\frac{11}{13}$
View full question & answer→Question 102 Marks
In a lottery there are $10$ prizes and $25$ blanks. What is the probability of getting a prize$?$
AnswerTotal no. of possible outcomes $= 35 \{10$ prizes, $25$ blanks$\}$
$E ⟶$ event of getting prize
No. of favourable outcomes $= 10 \{10$ prizes$\}$
Probability, $\text{P(E)}=\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}=\frac{10}{35}=\frac{2}{7}$
View full question & answer→Question 112 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Either a black card or a king.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Either a black card of a king
$m =$ there are $26$ black cards and $2$ red kings
$= 26 + 2 = 28$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{28}{52}=\frac{7}{13}$
View full question & answer→Question 122 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Neither an ace nor a king.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Total number of ace card are $4$ and king are $4$
Total number of cards that are a ace and a king is equal to $4 + 4 = 5$
Hence Total number of cards that are neither an ace nor a kin is $52 - 8 = 44$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting cards neither an ace nor a king $=\frac{44}{52}=\frac{11}{13}$
View full question & answer→Question 132 Marks
If the probability of winning a game is $0.3,$ what is the probability of loosing it$?$
AnswerGiven: Probability of winning a game $P(E) = 0.3$
To Find: Probability of losing the game $\text{P}(\bar{\text{E}})$
Calculation: We know that sum of probability of occurrence of an event and probability of non occurrence of an event is $1.$
$\text{P(E)}+\text{P}(\bar{\text{E}})=1$
$0.3+\text{P}(\bar{\text{E}})=1$
$\text{P}(\bar{\text{E}})=1-0.3$
$\text{P}(\bar{\text{E}})=0.7$
Hence the probability of losing the game is $\text{P}(\bar{\text{E}})=0.7$.
View full question & answer→Question 142 Marks
Cards each marked with one of the numbers $4, 5, 6, ....., 20$ are placed in a box and mixed thoroughly. One card is drawn at random from the box what is the probability of getting an even number$?$
AnswerNo. of card having marks from $4$ to $20 (n) = 17$
One card is drwan at random
Even numbers on the cards are $4, 6, 8, 10, 12, 14, 16, 18, 20$
Total $(m) = 9$
$\therefore\ \text{Probability}=\frac{\text{m}}{\text{n}}=\frac{9}{17}$
View full question & answer→Question 152 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A ten.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Total number of ten is $4$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting a ten is $\frac{4}{52}=\frac{1}{13}$
View full question & answer→Question 162 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Neither a heart nor a king.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Neither a heart nor a king:
There are $13$ cards of heart and $3$ kings more
i.e., $13 + 3 = 16$ total
$\therefore m =$ cards other than the above
$= 52 - 16 = 36$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{36}{52}=\frac{9}{13}$
View full question & answer→Question 172 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A black card.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E ⟶$ event of getting a black card.
No. of favourable outcomes $= 26 \{13$ cards of spades & $13$ cards of clubs$\}$
$\text{P(E)}=\frac{26}{52}=\frac{1}{2}$
View full question & answer→Question 182 Marks
A die is thrown once. What is the probability of getting a number lying between $2$ and $6?$
AnswerTotal numbers on the die $= 6 ($from $1$ to $6)$
$\therefore$ Probability of number lying between $2$ and $6$
$(\text{i.e. }3, 4, 5)=\frac{3}{6}=\frac{1}{2}$
View full question & answer→Question 192 Marks
In a class, there are $18$ girls and $16$ boys. The class teacher wants to choose one pupil for class monitor. What she does, she writes the name of each pupil on a card and puts them into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:
- The name of a girl.
- The name of a boy.
AnswerNo. of student in a class $(n)$
$= 18$ girls $+\ 16$ boys $= 34$
One students is to be a class monitor
- No. of girls $(m) = 18$
$\therefore$ Probability of being a girls as monitor of the
$\text{class}=\text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{18}{34}=\frac{9}{17}$
- No. of boys $(m) = 16$
$\therefore$ Probability of being a boy as monitor of the
$\text{class}=\text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{16}{34}=\frac{8}{17}$ View full question & answer→Question 202 Marks
One card is drawn from a well shuffled deck of $52$ playing cards. What is the probability of getting a non-face card$?$
AnswerNo. of cards in the deck of playing cards $(n) = 52$
No. of face cards $= 3 × 4 = 12$
Remaining non-face cards $= 52 - 12 = 40$
$\therefore$ Probability of non-face card $=\frac{40}{52}=\frac{10}{13}$
View full question & answer→Question 212 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Spade or an ace.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E ⟶$ event of getting spade or an all.
No. of favourable outcomes $= 13 + 3 = 16 \{13$ spades & $3$ aces each of hearts, diamonds & clubs$\}$
$\text{P(E)}=\frac{16}{52}=\frac{4}{13}$
View full question & answer→Question 222 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A jack, queen or a king.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
A jack, queen or a king are $3$ from each $4$ suits
Total number of a jack, queen and king are $12$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting a jack, queen or a king is $=\frac{12}{52}=\frac{3}{13}$
View full question & answer→Question 232 Marks
There are $30$ cards, of same size, in a bag on which numbers $1$ to $30$ are written. One card is taken out of the bag at random. Find the probability that the number on the selected card is not divisible by $3.$
AnswerTotan numbar of cards bearing numbers from $1$ to $30 (n) = 30$
Now numbers which are divisible by $3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,$ which are $10$
$\therefore$ Numbers which are not divisible by $3(n) = 30 - 10 = 20$
Now probability $\text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{20}{30}=\frac{2}{3}$
View full question & answer→Question 242 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A spade.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
A spade : There are $13$ cards of spade
$\therefore m = 13$
$\text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{13}{52}=\frac{1}{4}$
View full question & answer→Question 252 Marks
An urn contains $10$ red and $8$ white balls. One ball is drawn at random. Find the probability that the ball drawn is white.
AnswerTotal no of possible outcomes $= 18 \{10$ red balls, $8$ white balls$\}$
$E ⟶$ event of drawing white ball
No. of favourable outcomes $= 8 \{8$ white balls$\}$
Probability, $\text{P(E)}=\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}$
$=\frac{8}{18}=\frac{4}{9}$
View full question & answer→Question 262 Marks
A number is chosen at random from the number $-3, -2, -1, 0, 1, 2, 3.$ What will be the probability that square of this number is less then or equal to $1?$
Answer$S = \{-3, -2, -1, 0, 1, 2, 3\}$
Let $E$ be the event of getting a number whose square is less than or equal to $1.$
So, $E = \{-1, 1, 0\}$
$\text{P(E)}=\frac{3}{7}$
Hence, the probability of getting a number whose square is less than or equal to is $\frac{3}{7}$.
View full question & answer→Question 272 Marks
Five cards the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
- What is the probability that the card is the queen?
- If the queen is drawn and put a side, what is the probability that the second card picked up is:
- An ace$?$
- A queen$?$
Answer$5$ cards are the ten, jack, queen, king ace $(n) = 5$
One card is picked up at random:
- Probability of a card being a queen $=\frac{\text{m}}{\text{n}}=\frac{1}{5}$
- Queen is drawn and put aside, then number of cards will be $= 4$
- Probability of card being a ace $=\frac{\text{m}}{\text{n}}=\frac{1}{4}$
- Probability of card being a queen $=\frac{\text{m}}{\text{n}}=\frac{0}{4}=0$
View full question & answer→Question 282 Marks
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than $10.$
AnswerWhen a pair of dice are thrown, then total no. of possible outcomes $= 6 × 6 = 36$
let $E ⟶$ event of getting sum on dice greater than $10$
Then no of favourable outcomes $= 3 \{(5, 6) (6, 5) (6, 6)\}$
We know that, $\text{P(E)}=\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}$
i.e., $\text{P(E)}=\frac{3}{36}=\frac{1}{12}$
View full question & answer→Question 292 Marks
A bag contains $5$ red, $8$ green and $7$ white balls, One ball is drawn at random from the bag. What is the probability of getting a white ball or a green ball$?$
AnswerGiven: A bag contains $5$ red, $8$ green and $7$ white balls
To Find: Probability of getting a white ball or a green ball.
Total number of balls $5 + 8 + 7 = 20$
Total number of green or white balls $8 + 7 = 15$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting a green or a white ball $=\frac{15}{20}=\frac{3}{4}$
Hence probability of getting an green or white ball $=\frac{3}{4}$
View full question & answer→Question 302 Marks
Tickets numbered $1$ to $20$ are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of $3?$
AnswerTotal number of tickets $($from $1$ to $20) = 20$
One ticket is drawb at random
Number which are nultiple of $3$ are $: 3, 6, 9, 12, 15, 18$
Total numbers $(m) = 6$
$\therefore\ \text{Probability}=\frac{\text{m}}{\text{n}}=\frac{6}{20}=\frac{3}{10}$
View full question & answer→Question 312 Marks
What is the probability that a number selected at random from the number $1, 2, 2, 3, 3, 3, 4, 4, 4, 4$ will be their average$?$
AnswerGiven: A number is selected from the numbers $1, 2, 2, 3, 3, 3, 4, 4, 4, 4$
To Find: Probability that the selected number is the average of the numbers
Total numbers are $10$
Average of numbers is
$=\frac{1+2+2+3+3+3+4+4+4+4}{10}$
$=\frac{30}{10}$
$=3$
Total numbers of numbers which are average of these numbers are $3$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence Probability that the selected number is the average of the numbers $=\frac{3}{10}$
View full question & answer→Question 322 Marks
All kings and queens are removed from a pack of $52$ cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this card is:
- A red face card.
- A black card.
AnswerAll king and all Queens are removed then the remaining cards $= 52 - 8 = 44$
- A red face cards are $= 2$
$\therefore\ \text{Pribability}=\frac{2}{44}=\frac{1}{22}$
- A black cards are $= 26 - 4 = 22$
$\therefore$ Probability of a black cards $=\frac{22}{44}=\frac{1}{2}$ View full question & answer→Question 332 Marks
Die is thrown once. Find the probability of getting a number less than $3.$
AnswerGiven: A dice is thrown once
To Find: Probability of getting a number less than $3$
Total number on a dice is $6.$
Number less than $3$ are $1$ and $2$
Total number of numbers less than $3$ is $2$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting a number less than $3$ is equal to $\frac{2}{6}=\frac{1}{3}$
Hence probability of getting a number less than $3=\frac{1}{3}$
View full question & answer→Question 342 Marks
All jacks, queens and kings are removed from a pack of $52$ cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this cards is:
- A black face card.
- A red card.
AnswerAll jacks, queen and kings are removed
$\therefore$ Remaining cards $= 52 - 4 × 3 = 52 - 12 = 40$
- A black face cards $= 0$
$\therefore$ Probability $= 0$
- A red car $= 20$
$\therefore\ \text{probability}=\frac{20}{40}=\frac{1}{2}$ View full question & answer→Question 352 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Other than an ace.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E ⟶$ event of getting card other than an ace.
No. of favourable outcomes $= 52 - 4 = 48\{$Since we have $4$ ace cards$\}$
$\text{P(E)}=\frac{48}{52}=\frac{12}{13}$
View full question & answer→Question 362 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
The ace of spades.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E ⟶$ event of getting the ace of spades.
No. of favourable outcomes $= 1\{$ace of spades$\}$
$\text{P(E)}=\frac{1}{52}$
View full question & answer→Question 372 Marks
Two coins are tossed simultaneously. What is the probability of getting at least one head$?$
AnswerGiven: Two coins are tossed simultaneously.
To Find: Probability of getting at least one head.
When two coins are tossed then the outcome will be
$TT, HT, TH, HH.$
Hence total number of outcome is $4.$
At least one head means $1H$ or $2H.$
Hence total number of favorable outcome i.e. at least one head is $3$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting at least one head $=\frac{3}{4}$
View full question & answer→Question 382 Marks
What is the probability that a leap year has $53$ Sundays and $53$ Mondays$?$
AnswerA leap year has $366$ days i.e. $52$ weeks and $2$ days
When a leap year has $53$ Sundays and $53$ Mondays
$\therefore m = 1$ and $n = 7$
$\therefore\ \text{P(A)}=\frac{1}{7}$
View full question & answer→Question 392 Marks
Find the probability that a number selected from the number $1$ to $25$ is not a prime number when each of the given numbers is equally likely to be selected.
AnswerGivne: A number is selected from numbers $1$ to $25$
To Find: Probability of getting a number which is not a prime.
Total number of cards is $25.$
Total number of elementary events $= 25$
Cards bearing non prime numbers are $1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25$
Total number of cards bearing non-prime numbers $= 16$
Number of favourable elementary events $= 16$
We know that, $\text{Probability}=\frac{\text{number of favourable elementary events}}{\text{Total number of elementary events}}$
So, $P($getting a card bearing a non prime number$) =\frac{16}{25}$
View full question & answer→Question 402 Marks
It is given that in a group of $3$ students, the probability of $2$ students not having the same birthday is $0.992.$ What is the probability that the $2$ students have the same birthday$?$
AnswerLet $E ⟶$ event of $2$ students having same birthday $P(E)$ is given as $0.992$
Let $(\bar{\text{E}})\rightarrow$ event of $2$ students not having same birthday.
We know that, $\text{P}(\text{E})+\text{P}(\bar{\text{E}})=1$
$\text{P}(\bar{\text{E}})=1-\text{P(E)}$
$=1-0.992$
$=0.008$
View full question & answer→Question 412 Marks
A bag contains $5$ white and $7$ red balls. One ball is drawn at random. What is the probability that ball drawn is white$?$
AnswerTotal no. of possible outcomes $= 12 \{5$ white, $7$ red$\}$
$E ⟶$ event of drawing white ball.
No. of favorable outcomes $= 5 \{$white balls are $5\}$
Probability, $\text{P(E)}=\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}$
$\text{P(E)}=\frac{5}{12}$
View full question & answer→Question 422 Marks
Why is tossing a coin considered to be a fair way of deciding which team should choose ends in a game of cricket$?$
AnswerNo. of possible outcomes while tossing a coin $= 2 \{1$ head & $1$ tail$\}$
$\text{P(E)}=\frac{\text{No. of favorable outcomes}}{\text{Total no. of possible outcomes}}$
$\text{P(getting head)}=\frac{1}{2}$
$\text{P(getting tail)}=\frac{1}{2}$
Since probability of two events are equal, these are called equally like events.
Hence, tossing a coin is considered to be a fair way of deciding which team should choose ends in a game of cricket.
View full question & answer→Question 432 Marks
What is the probability that a number selected from the numbers $1, 2, 3, ....., 15$ is a multiple of $4?$
AnswerNumbers are $1, 2, 3, ....., 15$
$\therefore n = 15$
Now multiple of $4$ are $4, 8, 19$
$\therefore m = 3$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{3}{15}=\frac{1}{5}$
View full question & answer→Question 442 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Black and a king.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E ⟶$ event of getting black & a king.
No. of favourable outcomes $= 2 \{$king of spades & clubs$\}$
$\text{P(E)}=\frac{2}{52}=\frac{1}{26}$
View full question & answer→Question 452 Marks
The faces of a red cube and a yellow cube are numbered from $1$ to $6.$ Both cubes are rolled. What is the probability that the top face of each cube will have the same number$?$
AnswerTwo cubes bearing numbers $1$ to $6$ each, are rolled
$\therefore$ Number of total outcomes $= 6 × 6 = 36$
Now probability of comming of two same number i.e. $(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)$ can be
$\text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{6}{36}=\frac{1}{6}$
View full question & answer→Question 462 Marks
A die is thrown once. What is the probability of getting an odd number$?$
AnswerGiven: A dice is thrown once
To Find: Probability of getting an odd number.
Total number on a dice is $6.$
Odd numbers on a dice are $1, 3$ and $5$
Total number of odd numbers on dice is $3$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of an odd number $=\frac{3}{6}=\frac{1}{2}$
Hence probability of getting an odd number $=\frac{1}{2}$
View full question & answer→Question 472 Marks
The probability that it will rain tomorrow is $0.85.$ What is the probability that it will not rain tomorrow$?$
AnswerLet $E$ be the event of happening of rain
$P(E)$ is given as $0.85$
$E^-⟶ ??? ℎ????????\ ??\ ????$
$P(E^-) = 1 - P(E) = 1 - 0.85 = 0.15$
$\therefore P($not happening of rain$) = 0.15$
View full question & answer→Question 482 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
Neither a red card nor a queen.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
Neither a red card nor a queen
There are $26$ red card and two black queens more
$\therefore m = 52 - (26 + 2) = 52 - 28 = 24$
$\therefore\ \text{P(A)}=\frac{\text{m}}{\text{n}}=\frac{24}{52}=\frac{6}{13}$
View full question & answer→Question 492 Marks
A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is:
A red card.
AnswerGiven: A card is drawn at random from a pack of $52$ cards
To Find: Probability of the following
Total number of cards $= 52$
$E →$ event of getting a red card.
No. of favourable outcomes $= 26\{13$ hearts, $13$ diamonds$\}$
$\text{P(E)}=\frac{26}{52}=\frac{1}{2}$
View full question & answer→Question 502 Marks
What is the probability that an ordinary year has $53$ Sundays$?$
AnswerGiven: An ordinary year
To Find: Probability that a non leap year has $53$ Sundays.
Total number of days in an ordinary year is $365$ days
Hence number of weeks in an ordinary year is $\frac{365}{7}=52\text{ weeks and 1 day}$
In an ordinary year we have $52$ complete weeks and $1$ day which can be any day of the week i.e. $\text{SUNDAY, MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY and SATURDAY}$
To make $53$ Sundays the additional day should be Sunday
Hence total number of days is $7$
Favorable day i.e. Sunday is $1$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability that an ordinary year has $53$ Sundays is equal to $\frac{1}{7}$
View full question & answer→