Probability (Class 12)

JEE Main 2025 (Online) 28th January Morning ShiftMCQEasy📈 Topic in 13% papers+4−1

Ques. 1JEE Main 2025, 28 January (Morning Shift)

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denotes the number of defective oranges, then the variance of x is

26/75
14/25
18/25
28/75

Answer

(4) 28/75

Solution

Total ways = 10C2 = 45

P(x = 0) = 7C245 = 2145, P(x = 1) = 3 745 = 2145, P(x = 2) = 3C245 = 345

E(x) = 0 + 21 + 645 = 2745 = 35

E(x2) = 0 + 21 + 1245 = 3345 = 1115

Var(x) = E(x2) - [E(x)]2 = 1115 - 925

= 55 - 2775 = 2875

Answer: (4)

Keep practising — Probability (Class 12)

Ques. 2JEE Main 2025, 28 January (Evening Shift)

Bag B1 contains 6 white and 4 blue balls, Bag B2 contains 4 white and 6 blue balls, and Bag B3 contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag B2 is:

Ques. 3JEE Main 2025, 24 January (Morning Shift)

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability, that A wins if A makes the first throw, is

Ques. 4JEE Main 2025, 22 January (Morning Shift)

A coin is tossed three times. Let X denote the number of times a tail follows a head. If and 2 denote the mean and variance of X, then the value of 64 ( + 2 ) is:

Ques. 5JEE Main 2025, 22 January (Morning Shift)

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is mn, where (m,n)=1, then m+n is equal to :

Ques. 6JEE Main 2025, 22 January (Evening Shift)

If A and B are two events such that P(A B)=0.1, and P(A B) and P(B A) are the roots of the equation 12x2-7x+1=0, then the value of P( A B)P( A B) is :

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