JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Probability

WhatsApp Email

The probabilities that players A and B of a team are selected for the captaincy for a tournament are 0.6 and 0.4 , respectively. If A is selected the captain, the probability that the team wins the tournament is 0.8 and if B is selected the captain, the probability that the team wins the tournament is 0.7 Then the probability, that the team wins the tournament, is :

(A)0.74
(B)0.76✓ Correct
(C)0.72
(D)0.78

Answer: (B)

Solution

By the law of total probability, the team's chance of winning is

P (A) P (win ∣ A) + P (B) P (win ∣ B) = 0.6 \times 0.8 + 0.4 \times 0.7 = 0.48 + 0.28 = 0.76

. The probability that the team wins is

0.76

JEE Main · 2026 · 05 Apr 2026 · 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 →