JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Probability

There are three bags

X, Y

and

Z

. Bag

X

contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag Y , is :

(A) $\frac{1}{3}$ ✓ Correct
(B) $\frac{1}{2}$
(C) $\frac{1}{4}$
(D) $\frac{5}{12}$

Answer: (A)

Solution

By Bayes' theorem,

P (Y ∣ 1-rupee drawn) = \frac{P ( Y ) P ( 1 -rupee ∣ Y )}{\sum P ( bag ) P ( 1 -rupee ∣ bag )}

.
Each bag equally likely (

1/3

);

P (1 -rupee ∣ X) = 5/9

P (1 -rupee ∣ Y) = 4/9

P (1 -rupee ∣ Z) = 3/9

P (Y ∣ 1 -rupee) = \frac{4/9}{5/9 + 4/9 + 3/9} = \frac{4}{12} = \frac{1}{3}

JEE Main · 2024 · 08 Apr 2024 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Probability →

More JEE Main questions on Probability

A random variable $X$ takes values $0, 1, 2, 3$ with probabilities $\frac{2 a + 1}{30}$ , $\frac{8 a - 1}{30}$ , $\frac{4 a + 1}{30}$ , b respectively, where $a, b \in R$ . Let $μ$ and $σ$ respectively be the mean and standard deviation of X such that $σ^{2} + μ^{2} = 2$ .
Then …
JEE Main 2026View solution →
Two distinct numbers a and b are selected at random from $1, 2, 3, \dots, 50$ . The probability, that their product ab is divisible by 3, is
JEE Main 2026View solution →
If a random variable $x$ has the probability distribution
x 0 1 2 3 4 5 6 7
$p (x)$ 0 $2 k$ $k$ $3 k$ $2 k^{2}$ $2 k$ $k^{2} + k$ $7 k^{2}$

then …
JEE Main 2026View solution →
From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that $a - b \geq 10$ is $\frac{m}{n}, gcd (m, n) = 1$ , then $m + n$ is equal to ______.
JEE Main 2026View solution →
Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is …
JEE Main 2026View solution →
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-
JEE Main 2026View solution →