If A and B are two independent events with $\text{P(A)}=\frac{1}{3}$ and $\text{P(B)}=\frac{1}{4},$ then P(B'|A) is equal to:
View full solution →- $\frac{1}{4}$
- $\frac{1}{3}$
- $\frac{3}{4}$
- $1$
Question types
Probability question types
810 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
810
Questions
8
Question groups
5
Question types
01
M.C.Q (1 Marks)
172 Q→021 Marks Question
28 Q→032 Marks Questions
117 Q→043 Marks Question
183 Q→055 Marks Questions
275 Q→06Case study (4 Marks)
21 Q→07Fill In The Blanks[1 Marks ]
5 Q→08True False[1 Marks ]
9 Q→Sample Questions
Probability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If P(A) + P(B) = 1; then which of the following option explains the event A and B correctly?
- Event A and B are mutually exclusive, exhaustive and complementary events.
- Event A and B are mutually exclusive and exhaustive events.
- Event A and B are mutually exclusive and complementary events.
- Event A and B are exhaustive and complementary events.
Choose the correct answer from the given four options.
For the following probability distribution $E(X^2)$ is equal to:
| $\text{X}$ | $1$ | $2$ | $3$ | $4$ |
| $\text{P}(\text{X})$ | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
- A$3.$
- B$5.$
- C$7.$
- ✓$10.$
Answer: D.
View full solution →Choose the correct answer from the given four options.
If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:
View full solution →If A and B are two independent events with $\text{P}(\text{A})=\frac{3}{5}$ and $\text{P}(\text{A})=\frac{4}{9},$ then $\text{P}(\text{A'}\cap\text{B'})$ equals:
- $\frac{4}{15}$
- $\frac{8}{45}$
- $\frac{1}{3}$
- $\frac{2}{9}$
Choose the correct answer from the given four options.
For the following probability distribution E(X) is equal to:
|
X
|
-4
|
-3
|
-2
|
-1
|
0
|
|
P(X)
|
0.1
|
0.2
|
0.3
|
0.2
|
0.2
|
- 0
- -1
- -2
- -1.8
Two cards are drawn at random and one-by-one without replacement from a well-shuffled pack of 52 playing cards. Find the probability that one card is red and the other is black.
Compute $\text{P}(\text{A}|\text{B})\ \text{if}\ \text{P}(\text{B})=0.5\ \text{and}\ \text{P}(\text{A}\cap\text{B})=0.32$
View full solution →If $\text{P}(\text{A})=\frac{3}{5}\text{and}\ \text{P}(\text{B})=\frac{1}{5}$, find $\text{P}(\text{A}\cap\text{B})$ if A and B are independent events.
View full solution →Evaluate $\text{P}(\text{A}\cap\text{B})\ \text{if}\ 2\text{P}(\text{A})=\text{P}(\text{B})=\frac{5}{13}\ \text{and}\ \text{P}(\text{A}|\text{B})=\frac{2}{5}.$
View full solution →The probability distribution of random variable X is given below:
Find $\text{P}(\text{X}\leq2)+\text{P}(\text{X}>2)$
View full solution →|
$\text{X}$
|
$0$
|
$1$
|
$2$
|
$3$
|
|
$\text{P}(\text{X})$
|
$\text{k}$
|
$\frac{\text{k}}{2}$
|
$\frac{\text{k}}{4}$
|
$\frac{\text{k}}{8}$
|
A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green, is tossed. Let A be the event ‘‘number obtained is even’’ and B be the event ‘‘number obtained is red’’. Find if A and B are independent events.
$\text{If P(A) = 0·4, P(B) = p, P(A}\cup \text{B) = 0·6}$ and A and B are given to be independent events, find the value of ‘p’.
View full solution →Prove that if E and F are independent events, then the events E and F' are also independent.
A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event “number is even” and B be the event “number is marked red”. Find whether the events A and B are independent or not.
Determine the binomial distribution for which the mean is $20$ and variance $16.$
View full solution →An urn contains 4 red and 7 blue balls. Two balls are drawn at random with replacement. Find the probability of getting:
- 2 red balls.
- 2 blue balls.
- One red and one blue ball.
Two dice are thrown together. What is the probability that the sum of the numbers on the two dice is neither 9 nor 11?
There are two bags $I$ and $II.$ Bag I contains $3$ white and $4$ red balls and Bag $II$ contains $5$ white and $6$ red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag $II.$
View full solution →Find the mean $\mu $ variance $\sigma ^2$ for the following probability distribution:
View full solution →| $X$ | $0$ | $1$ | $2$ | $3$ |
| $P(X)$ | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{3}{10}$ | $\frac{1}{30}$ |
In a game, a man wins ₹ 5 for getting a number greater than 4 and loses ₹ 1 otherwise, when a fair die is thrown. The man decided to throw a die three but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.
Of the students in a school, it is known that $30\%$ have $100\%$ attendanceand $70\%$ students are irregular. Previous year results report that $70\%$ of all students who have $100\%$ attendance attain A grade and $10\%$ irregular students attain A grade in their annual examination. At the end of the year, one student is chosen at random from the school and he was found to have an A grade. What is the probability that the student has $100\%$ attendance? Is regularity required only in school? Justify your answer.
View full solution →There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean and variance of X.
Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ₹ x each, ₹ y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹ 1,600. School B wants to spend ₹ 2,300 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹ 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.
Two numbers are selected at random $($without replacement$)$ from the first six positive integers. Let $X$ denote the larger of the two numbers obtained. Find the probability distribution of the random variable $X,$ and hence find the mean of the distribution.
View full solution →In a family there are four children. All of them have to work in their family business to earn their livelihood at the age of 18. 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- Probability that all children are girls, if it is given that elder child is a boy, is:
- $\frac{3}{8}$
- $\frac{1}{8}$
- $\frac{5}{8}$
- None of these.
- Probability that all children are boys, if two elder children are boys, is:
- $\frac{1}{4}$
- $\frac{3}{4}$
- $\frac{1}{2}$
- None of these.
- Find the probability that two middle children are boys, if it is given that eldest child is a girl.
- $0$
- $\frac{3}{4}$
- $\frac{1}{4}$
- None of these.
- Find the probability that all children are boys, if it is given that at most one of the children is a girl.
- $0$
- $\frac{1}{5}$
- $\frac{2}{5}$
- $\frac{4}{5}$
- Find the probability that all children are boys, if it is given that at least three of the children are boys.
- $\frac{1}{5}$
- $\frac{2}{5}$
- $\frac{3}{5}$
- $\frac{4}{5}$
Suman was doing a project on a school survey, on the average number of hours spent on study by students selected at random. At the end of survey, Suman prepared the following report related to the data. Let X denotes the average number of hours spent on study by students. The probability that X can take the values x, has the following form, where k is some unknown constant.$\text{P(X}=\text{x})\begin{cases}0.2,\text{if x}= 0\\\text{kx},\text{if}\text{ x}=1\text{ or }2\\\text{k}(6-\text{x}),\text{if}\text{ x}=3\text{ or }4\\0,\text{odherwise}\end{cases}$
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- Find the value of k.
- 0.1
- 0.2
- 0.3
- 0.05
- What is the probability that the average study time of students is not more than 1 hour?
- 0.4
- 0.3
- 0.5
- 0.1
- What is the probability that the average study time of students is at least 3 hours?
- 0.5
- 0.9
- 0.8
- 0.1
- What is the probability that the average study time of students is exactly 2 hours?
- 0.4
- 0.5
- 0.7
- 0.2
- What is the probability that the average study time of students is at least 1 hour?
- 0.2
- 0.4
- 0.8
- 0.6
To teach the application of probability a maths teacher arranged a surprise game for 5 of his students namely Archit, Aadya, Mivaan, Deepak and Vrinda. He took a bowl containing tickets numbered 1 to 50 and told the students go one by one and draw two tickets simultaneously from the bowl and replace it after noting the numbers. 
Based on the above information, answer the following questions.
View full solution → Based on the above information, answer the following questions.
- Teacher ask Vrinda, what is the probability that both tickets drawn by Arch it shows even number?
- $\frac{1}{50}$
- $\frac{12}{49}$
- $\frac{13}{49}$
- $\frac{15}{49}$
- Teacher ask Mivaan, what is the probability that both tickets drawn by Aadya shows odd number?
- $\frac{1}{50}$
- $\frac{2}{49}$
- $\frac{12}{49}$
- $\frac{5}{49}$
- Teacher ask Deepak, what is the probability that tickets drawn by Mivaan, shows a multiple of 4 on one ticket and a multiple 5 on other ticket?
- $\frac{14}{245}$
- $\frac{16}{245}$
- $\frac{24}{245}$
- None of these.
- Teacher ask Arch it, what is the probability that tickets are drawn by Deepak, shows a prime number on one ticket and a multiple of 4 on other ticket?
- $\frac{3}{245}$
- $\frac{17}{245}$
- $\frac{18}{245}$
- $\frac{36}{245}$
- Teacher ask Aadya, what is the probability that tickets drawn by Vrinda, shows an even number on first ticket and an odd number on second ticket?
- $\frac{15}{98}$
- $\frac{25}{98}$
- $\frac{35}{98}$
- None of these.
A phannaceutical company wants to advertise a new product on T.V., where the product is specially designed for women. For that an advertising executive is hired to study television-viewing habits of married couples during prime time hours. Based on past viewing records he has determined that during prime time husbands are watching television 70% of the time. It has also been determined that when the husband is watching television, 30% of the time the wife is also watching. When the husband is not watching television, 40% of the time the wife is watching television. Based on the above information, answer the following questions.
View full solution →- The probability that the husband is not watching television during prime time, is:
- 0.6
- 0.3
- 0.4
- 0.5
- If the wife is watching television, the probability that husband is also watching television, is:
- $\frac{2}{11}$
- $\frac{7}{11}$
- $\frac{5}{11}$
- $\frac{8}{11}$
- The probability that both husband and wife are watching television during prime time, is:
- 0.21
- 0.5
- 0.3
- 0.4
- The probability that the wife is watching television during prime time, is:
- 024
- 0.33
- 0.3
- 0.4
- If the wife is watching television, then the probability that husband is not watching television, is:
- $\frac{2}{11}$
- $\frac{4}{11}$
- $\frac{1}{11}$
- $\frac{5}{11}$
A student is preparing for the competitive examinations LIC AAO, SSC CGL and Bank P.O. The probabilities that the student is selected independently in competitive examination of LIC AAO, SSC CGL and Bank P.O. are a, band c respectively. Of these examinations, students has 50% chance of selection in at least one, 40% chance of selection in at least two and 30% chance of selection in exactly two examinations.
Based on the above information, answer the following questions.
Based on the above information, answer the following questions.
- The value of a+ b + e - ab - be - ca + abe is:
- 0.3
- 0.5
- 0.7
- 0.6
- The value of ab + be + ae - 2abe is:
- 0.5
- 0.3
- 0.4
- 0.6
- The value of abe is:
- 0.1
- 0.5
- 0.7
- 0.3
- The value of ab + be + ae is:
- 0.1
- 0.6
- 0.5
- 0.3
- The value of a + b + e is:
- 1
- 1.5
- 1.6
- 1.4
Fill in the blanks.
If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
View full solution →If A and B are two events such that $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{p},\text{P}(\text{A})=\text{p},\text{P}(\text{B})=\frac{1}{3}$ and $\text{P}(\text{A}\cap\text{B})=\frac{5}{9},$ then p = __________.
Fill in the blanks.
Let $X$ be a random variable taking values $x_1, x_2, ......, x_n$ with probabilities $p_1, p_2, ..., p_n,$ respectively. Then var $(X) =$ ________.
View full solution →Let $X$ be a random variable taking values $x_1, x_2, ......, x_n$ with probabilities $p_1, p_2, ..., p_n,$ respectively. Then var $(X) =$ ________.
Fill in the blanks.
Let A and B be two events. If $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{P}(\text{A}),$ then A is _________ of B.
View full solution →Let A and B be two events. If $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\text{P}(\text{A}),$ then A is _________ of B.
Fill in the blanks.
If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9, P (X = 3), then p = _________.
If X follows binomial distribution with parameters n = 5, p and P (X = 2) = 9, P (X = 3), then p = _________.
Fill in the blanks.
If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
View full solution →If A and B are such that $\text{P}(\text{A}'\cup\text{B}')=\frac{2}{3}$ and $\text{P}(\text{A}\cup\text{B})=\frac{5}{9},$ then $\text{P}(\text{A}')+\text{P}(\text{B}')=$ ________.
State True or False for the statements:
If A and B are two independent events then P(A and B) = P(A) × P(B).
If A and B are two independent events then P(A and B) = P(A) × P(B).
State True or False for the statements:
If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)\geq1-\frac{\text{P}(\text{B}')}{\text{P}(\text{A})}.$
View full solution →If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)\geq1-\frac{\text{P}(\text{B}')}{\text{P}(\text{A})}.$
State True or False for the statements:
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
State True or False for the statements:
If A and B are independent, then.
P (exactly one of A, B occurs) = P(A)P(B') + P(B)P(A')
If A and B are independent, then.
P (exactly one of A, B occurs) = P(A)P(B') + P(B)P(A')
State True or False for the statements:
Two independent events are always mutually exclusive.
Two independent events are always mutually exclusive.
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