JEE MATH APEX

Probability-JEE-Mains-PYQ’s

Mathematics Questions

If A and B are two events such that P(A) = 0.7 , P(B) = 0.4 and P(A \cap \overline{B}) = 0.5 , where \overline{B} denotes the complement of B , then P(B \mid A \cup \overline{B}) is equal to:
(A) \frac{1}{2}
(B) \frac{2}{3}
(C) \frac{3}{4}
(D) \frac{1}{3}
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A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is \frac{n}{m}, where \gcd(m, n) = 1, then n^2 \cdot m^2 is equal to:
(A) 64
(B) 80
(C) 60
(D) 72
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Let a random variable X take values 0, 1, 2, 3 with P(X=0) = P(X=1) , P(X=2) = P(X=3) and E(X^2) = 2E(X) . Then the value of 8P-1 is:
(A) 2
(B) 0
(C) 3
(D) 1
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The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:
(A) \frac{1}{120}
(B) \frac{1}{60}
(C) \frac{1}{180}
(D) \frac{1}{182}
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A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let X denote the number of defective pens. Then the variance of X is:
(A) \frac{11}{18}
(B) \frac{2}{15}
(C) \frac{3}{5}
(D) \frac{28}{75}
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If the probability that the random variable X takes the value x is given by P(X = x) = k(x + 1)^2 , x = 0, 1, 2, 3 \ldots , where k is a constant, then P(X \geq 3) is equal to:
(A) \frac{1}{9}
(B) \frac{8}{27}
(C) \frac{7}{27}
(D) \frac{4}{9}
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Given three identical bags each containing 10 balls, whose colours are as follows:

BagRedBlueGreen
Bag I325
Bag II433
Bag III514

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from Bag I, and if the ball is Green, the probability that it is from Bag III is, then the value of \frac{1}{7} + \frac{1}{q} is:
(A) 6
(B) 9
(C) 7
(D) 8
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Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability that the ball drawn is white, is \frac{8}{17}, then n is equal to:
(A) 5
(B) 6
(C) 4
(D) 3
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Bag B_1 contains 5 white and 4 blue balls, Bag B_2 contains 4 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 B_2 is:
(A) \frac{4}{9}
(B) \frac{5}{13}
(C) \frac{1}{2}
(D) \frac{2}{3}
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Let S be the set of all words that can be formed by arranging all the letters of the word GARDEN. From this set S , one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:
(A) \frac{1}{6}
(B) \frac{5}{12}
(C) \frac{1}{3}
(D) \frac{2}{3}
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