Probability · Mathematics · KCET

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MCQ (Single Correct Answer)

1

A random experiment has five outcomes $\mathrm{w}_1, \mathrm{w}_2, \mathrm{w}_3, \mathrm{w}_4$ and $\mathrm{w}_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b$ and $\frac{1}{12}$ such that $12 a+12 b-1=0$. Then the probabilities of occurrence of the outcome $w_3$ is

KCET 2025
2

A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is

KCET 2025
3

Consider the following statements.

Statement (I): If E and F are two independent events, then $E^{\prime}$ and $F^{\prime}$ are also independent.

Statement (II): Two mutually exclusive events with non-zero probabilities of occurrence cannot be independent.

Which of the following is correct?

KCET 2025
4

If A and B are two non-mutually exclusive events such that $\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})$, then

KCET 2025
5
If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$, then which of the following is correct?
KCET 2025
6

Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is $\frac{2}{5}$. If she visits temple $A, \frac{1}{3}$ is the probability that she meets her friend, whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple B is

KCET 2025
7

A die is thrown 10 times. The probability that an odd number will come up at least once is

KCET 2024
8

A random variable $X$ has the following probability distribution:

$X$ 0 1 2
$P(X)$ 25/36 $k$ 1/36

If the mean of the random variable $X$ is $1 / 3$, then the variance is

KCET 2024
9

If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$, then $p$ is equal to

KCET 2024
10

A bag contains $$2 n+1$$ coins. It is known that $$n$$ of these coins have head on both sides whereas, the other $$n+1$$ coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $$\frac{31}{42}$$, then the value of $$n$$ is

KCET 2023
11

Let $$A=\{x, y, z, u\}$$ and $$B=\{a, b\}$$. A function $$f: A \rightarrow B$$ is selected randomly. The probability that the function is an onto function is

KCET 2023
12

If $$A$$ and $$B$$ are events, such that $$P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}$$ and $$P(B / A)=\frac{2}{3}$$, then $$P(B)$$ is

KCET 2023
13

Find the mean number of heads in three tosses of a fair coin.

KCET 2022
14

If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{2}, P(B)=\frac{1}{2}$$ and $$P(A \mid B)=\frac{1}{4}$$, then $$P\left(A^{\prime} \cap B^{\prime}\right)$$ is

KCET 2022
15

A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month is

KCET 2022
16

If $$A$$ and $$B$$ are two independent events such that $$P(\bar{A})=0.75, P(A \cup B)=0.65$$ and $$P(B)=x$$, then find the value of $$x$$.

KCET 2022
17

Given that, $$A$$ and $$B$$ are two events such that $$P(B)=\frac{3}{5}, P\left(\frac{A}{B}\right)=\frac{1}{2}$$ and $$P(A \cup B)=\frac{4}{5}$$, then $$P(A)$$ is equal to

KCET 2021
18

If $$A, B$$ and $$C$$ are three independent events such that $$P(A)=P(B)=P(C)=P$$, then $$P$$ (at least two of $$A, B$$ and $$C$$ occur) is equal to

KCET 2021
19

Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6 the probability of getting a sum as 3 is

KCET 2021
20

A car manufacturing factory has two plants $$X$$ and $$Y$$. Plant $$X$$ manufactures $$70 \%$$ of cars and plant $$Y$$ manufactures $$30 \%$$ of cars. $$80 \%$$ of cars at plant $$X$$ and $$90 %$$ of cars at plant $$Y$$ are rated as standard quality. A car is chosen at random and is found to be standard quality. The probability that it has come from plant $$X$$ is :

KCET 2021
21

If $$P(A)=0.59, P(B)=0.30$$ and $$P(A \cap B)=0.21$$ then $$P\left(A^{\prime} \cap B^{\prime}\right)$$ is equal to

KCET 2021
22

A die is thrown 10 times, the probability that an odd number will come up at least one time is

KCET 2020
23

If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$$ and $$P(A \cap B)=\frac{1}{6}$$, then $$P\left(A^{\prime} / B\right)$$ is

KCET 2020
24

Events $$E_1$$ and $$E_2$$ from a partition of the sample space $$S$$. $$A$$ is any event such that $$P\left(E_1\right)=P\left(\dot{E}_2\right)=\frac{1}{2}, P\left(E_2 / A\right)=\frac{1}{2}$$ and $$P\left(A / E_2\right)=\frac{2}{3}$$, then $$P\left(E_1 / A\right)$$ is

KCET 2020
25

The probability of solving a problem by three persons $$A, B$$ and $$C$$ independently is $$\frac{1}{2}, \frac{1}{4}$$ and $$\frac{1}{3}$$ respectively. Then the probability of the problem is solved by any two of them is

KCET 2020
26

If $$A, B, C$$ are three mutually exclusive and exhaustive events of an experiment such that $$P(A)=2 P(B)=3 P(C)$$, then $$P(B)$$ is equal to

KCET 2020
27

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is consonant is

KCET 2019
28

A random variable '$$X$$' has the following probability distribution

$$x$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$
$$P(x)$$ $$k-1$$ $$3k$$ $$k$$ $$3k$$ $$3k^2$$ $$k^2$$ $$k^2+k$$

Then the value of $$k$$ is

KCET 2019
29

If $$A$$ and $$B$$ are two events of a sample space $$S$$ such that $$P(A)=0.2, P(B)=0.6$$ and $$P(A \mid B)=0.5$$ then $$P\left(A^{\prime} \mid B\right)=$$

KCET 2019
30

If '$$X$$' has a binomial distribution with parameters $$n=6, p$$ and $$P(X=2)=12$$, $$P(X=3)=5$$ then $$P=$$

KCET 2019
31

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $$S=\{1,2,3,4,5,6,7\}$$ and reports that it is even. The probability that is actually even is

KCET 2019
32
A bag contains 17 tickets numbered from 1 to 17. A ticket is drawn at random, then another ticket is drawn without replacing the first one. The probability that both the tickets may show even numbers is
KCET 2018
33
A flashlight has 10 batteries out of which 4 are dead. If 3 batteries are selected without replacement and tested, then the probability that all 3 are dead is
KCET 2018
34
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
KCET 2018
35
In a simultaneous throw of a pair of dice, the probability of getting a total more than 7 is
KCET 2018
36
If $A$ and $B$ are mutually exclusive events, given that $P(A)=\frac{3}{5}, P(B)=\frac{1}{5}$, then $P(A$ or $B)$ is
KCET 2018
37
A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective, is
KCET 2017
38

The probability distribution of $X$ is

$$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.3 & k & 2 k & 2 k \\ \hline \end{array} $$

$$ \text { The value of } k \text { is } $$
KCET 2017
39
Two events $A$ and $B$ will be independent if
KCET 2017
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