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Probability Basic Applied Maths - Probability Basic

CBSE - STD 11 Science - Applied Maths (CBSE - English Medium). 29 questions in this chapter.

Question types

Probability Basic question types

29 questions across 7 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.

29
Questions
7
Question groups
5
Question types
Sample Questions

Probability Basic questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ1 Mark
If $M$ and $N$ are any two events, the probability that atleast one of them occurs is
  • A
    $P(M)+P(N)-2 P(M \cap N)$
  • ✓
    $P(M)+P(N)-P(M \cap N)$
  • C
    $P(M)+P(N)+P(M \cap N)$
  • D
    $P(M)+P(N)+2 P(M \cap N)$

Answer: B.

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Q 2MCQ1 Mark
The probability that atleast one of the events $A$ and $B$ occurs is 0.6 . If $A$ and $B$ occur simultaneously with probability 0.2 , then $P(\bar{A})+P(\bar{B})$ is equal to :
  • A
    0.4
  • B
    0.8
  • ✓
    1.2
  • D
    1.6

Answer: C.

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Q 3MCQ1 Mark
If the probabilities for A to fail in an examination is 0.2 and that for $B$ is 0.3 , then the probability that either $A$ or $B$ fails is
  • A
    $>0.5$
  • B
    0.5
  • ✓
    $\leq 0.5$
  • D
    $0$

Answer: C.

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Q 4MCQ1 Mark
If a single letter is selected at random from the word 'PROBABILITY', then the probability of vowels is
  • A
    $\frac{1}{3}$
  • ✓
    $\frac{4}{11}$
  • C
    $\frac{2}{11}$
  • D
    $\frac{3}{11}$

Answer: B.

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Q 52 Marks Questions2 Marks
Reporting time of an employee is given below :
DayMonTueWedThursFriSat
Time (a.m.)10:3510:2010:2210:2710:2510:40
 If the reporting time is $10: 30 a . m$., then find the probability of his coming late.
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Q 62 Marks Questions2 Marks
An experiment involves tossing of two coins and recording them in the following events
$A$ : no tail
$B$ : exactly one tail
$C$ : at least one tail.
write the sets representing events (i) $A$ and $C$ (ii) $A$ but not $B$.
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Q 72 Marks Questions2 Marks
In an experiment of rolling a fair $\operatorname{die}$, let $A, B$ and $C$ be three events defined as -
$A$ : a number which is a perfect square.
$B$ : a prime number.
$C$ : a number which is greater than 5 .
These events are mutually exclusive or exhaustive?
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Q 103 Marks Question3 Marks
If $E_1, E_2, E_3$ are three mutually exclusive events and exhaustive events of an experiment such that-
$2 P\left(E_1\right)=3 P\left(E_2\right)=P\left(E_3\right)$, then find $P\left(E_1\right)$.
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Q 125 Marks Questions5 Marks
Three coins are tossed simultaneously. Consider the event $E$ 'three heads or three tails,' $F$ 'at least two heads' and $G$ 'at most two heads'. Of the pairs $(E, F),(E, G)$ and $(F, G)$, which are independent ? Which are dependent?
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Q 135 Marks Questions5 Marks
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random. Find the probability that
(i) The student opted for NCC or NSS.
(ii) The student has opted for neither NCC nor NSS.
(iii) The student has opted for NSS but not NCC.
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Q 145 Marks Questions5 Marks
A fair coin is tossed four times, and a person win ₹ 1 for each head and lose ₹ 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.
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Q 155 Marks Questions5 Marks
If the letters of the word 'ASSASSINATION' are arranged at random. Find the probability that
(i) four $S$ 's come consecutively in the word.
(ii) two I's and two N's come together.
(iii) all $A$ 's are not coming together.
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Q 165 Marks Questions5 Marks
A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that
(i) all the three balls are white
(ii) all the three balls are red.
(iii) One ball is red and two balls are white.
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Q 17Fill in the blanks.1 Mark
The probability of happening of an event $A$ is 0.5 and that of $B$ is 0.3 . If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ is _________________
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Q 18Fill in the blanks.1 Mark
If $A$ and $B$ are two events associated with a random experiment such that $P(A)=0.3, P(B)=0.2$ and $P(A \cap B)=0.1$, then the value of $P(A \cap \bar{B})$ is _________________
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Q 19Fill in the blanks.1 Mark
If $e_1, e_2, e_3$, and $e_4$ are the four elementary outcomes in a sample space and $P\left(e_1\right)=0.1, P\left(e_2\right)=0.5$ and $P\left(e_3\right)=0.1$, then the probability of $e_4$ is _________________
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Q 20Fill in the blanks.1 Mark
The probability that the home team will win an upcoming football game is 0.77 , the probability that it will tie the game is 0.08 and the probability that it will lose the game is _________________
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Q 214 Marks Questions4 Marks
A young man visits a hospital for medical check up. The probability that he has lungs problem is 0.55 , heart problem is 0.29 and either lungs or heart problem is 0.57 . What is the probability that he has
(i) both type of problems : lungs as well as heart ?
(ii) lungs problem but not heart problem ?
Out of $1 0 0 0$ persons, how many are expected to have both type of problems?
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Q 24Match the following.4 Marks
Column - lColumn - ll
(a) If $E_1$ and $E_2$ are the two mutually exclusive events(i) $E_1 \cap E_2=E_1$
(b) If $E_1$ and $E_2$ are the mutually exclusive and exhaustive events(ii) $\left(E_1-E_2\right) \cup\left(E_1 \cap E_2\right)=E_1$
(c) If $E_1$ and $E_2$ have common outcomes, then If $E_1$ and $E_2$ are two events such that(iii) $E_1 \cap E_2=\phi, E_1 \cup E_2=S$,
(d) $E_1 \subset E_2$(iv) $E_1 \cap E_2=\phi$
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