If A and B are two events such that P(A) = 1/2, P(B) = 1/3, P(B, A) = 1/4, then P(A, B) is: Option 1: 1/8 Option 2: 7/8 Option 3: 3/8 Option 4: 5/8

Answer: 3/8. Solution: Given P(A) = 1/2, P(B) = 1/3, and P(B, A) = 1/4 To find P(A, B), we first need P(A B). Using the conditional probability formula: P(B, A) = (P(A B))/(P(A)) 1/4 = (P(A B))/(1/2) P(A B) = 1/4 x 1/2 P(A B) = 1/8 Now applying the conditional probability formula: P(A, B) = (P(A B))/(P(B)) P(A, B) = (1/8)/(1/3) P(A, B) = 1/8 x 3/1 P(A, B) = 3/8 Therefore, P(A, B) = 3/8

Algebra

Probability

Medium

core

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

$\frac{1}{8}$

$\frac{7}{8}$

$\frac{3}{8}$

$\frac{5}{8}$

✅ Correct Option: 3

Given $P(A) = \frac{1}{2}$ , $P(B) = \frac{1}{3}$ , and $P(B|A) = \frac{1}{4}$

To find $P(A|B)$ , we first need $P(A \cap B)$ .

Using the conditional probability formula:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$\frac{1}{4} = \frac{P(A \cap B)}{\frac{1}{2}}$

$P(A \cap B) = \frac{1}{4} \times \frac{1}{2}$

$P(A \cap B) = \frac{1}{8}$

Now applying the conditional probability formula:

$P(A|B) = \frac{P(A \cap B)}{P(B)}$

$P(A|B) = \frac{\frac{1}{8}}{\frac{1}{3}}$

$P(A|B) = \frac{1}{8} \times \frac{3}{1}$

$P(A|B) = \frac{3}{8}$

Therefore, $P(A|B) = \frac{3}{8}$

2022: 23 Aug Shift 1

In the family mother, father and son stand up at random for a family picture. Define following two events :

$E$ = [Son stands at one of the two ends in the picture]

$F$ = [Father stands in the middle of the picture]

The value of $P(F/E)$ is :

2026: 19 May Shift 2

A coin is tossed 5 times, the probability of getting at least 3 heads is:

2026: 26 May Shift 2

For a biased die, the probabilities of outcomes are given as under.

$P(1)=P(2)=\dfrac{2}{10}, P(3)=P(5)=P(6)=\dfrac{1}{10}, P(4)=\dfrac{3}{10}$ .

The die is thrown two times. Let A and B be events defined as

A is getting same number each time and

B is getting a total of 10 or more on die ,

then which one of the following is TRUE?

2024: 16 May Shift 1

There are $6$ cards numbered $1$ to $6$ , one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two cards drawn. Then $\mathrm{P}(\mathrm{X}>3)$ is :

2025: 22 May Shift 2

The probability distribution of a random variable x is given below.

x	0	1	2	3
P(x)	k/3	k/2	k/4	k/7

Then the value of k is

2026: 19 May Shift 1

A man is known to speak truth 8 out of 11 times. He takes out two balls from a bag containing 3 white, 2 black and 5 red balls. What is the probability that he reports both the balls to be white?

If A and B are two events such that P(A)=12P(A) = \frac{1}{2}P(A)=21​, P(B)=13P(B) = \frac{1}{3}P(B)=31​, P(B∣A)=14P(B|A) = \frac{1}{4}P(B∣A)=41​, then P(A∣B)P(A|B)P(A∣B) is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

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