Algebra

Probability

Medium

core

Bag I contains 2 red and 3 blue balls and bag II contains $\alpha$ red and 5 blue balls. One ball is drawn at random from one of the bags and is found to be blue. If the probability that it was drawn from bag II is $\frac{25}{52}$ , then $\alpha$ is equal to:

✅ Correct Option: 3

By Bayes' theorem, $\frac{\frac{1}{2}\cdot\frac{5}{\alpha+5}}{\frac{1}{2}\cdot\frac{3}{5}+\frac{1}{2}\cdot\frac{5}{\alpha+5}}=\frac{25}{52}$ .

Simplifying gives $\frac{25}{3(\alpha+5)+25}=\frac{25}{52}$ , so $3\alpha+15=27$ and $\alpha=4$ .

2026: 22 May Shift 1

Two dice are thrown simultaneously. If X denotes the number of sixes, then the mean of X is :

2026: 29 May Shift 1

Let A and B be two independent events such that $P(A)=k$ , $P(B)=2k$ and probability of occurrence of exactly one of them is $\dfrac{5}{9}$ . Then the value(s) of $k$ is/are:

2026: 22 May Shift 2

A bag contains 8 red and 7 black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is:

2025: 29 May Shift 2

A bag contain 8 blue and 12 green balls. Two balls are drawn in succession without replacement. The probability that first is blue and second is green is

2025: 13 May Shift 1

A random variable X has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	k²	2k²	7k² + k

The value of $P(4 < x < 7)$ is equal to

2025: 22 May Shift 2

Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag is selected at random and then a ball is drawn from it. The probability that the ball drawn is black is:

Bag I contains 2 red and 3 blue balls and bag II contains α\alphaα red and 5 blue balls. One ball is drawn at random from one of the bags and is found to be blue. If the probability that it was drawn from bag II is 2552\frac{25}{52}5225​, then α\alphaα is equal to:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Bag I contains 2 red and 3 blue balls and bag II contains $\alpha$ red and 5 blue balls. One ball is drawn at random from one of the bags and is found to be blue. If the probability that it was drawn from bag II is $\frac{25}{52}$ , then $\alpha$ is equal to: