Probability PYQs Set 16 (PDF)

Set 16 of 16 · Questions 451-458 of 458

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Probability · Set 16 (Q451-458)
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451. $A boy speaks truth in 3 out of 5 times. If he throws a die and tells that the number appeared on it is five, then the probability that it is actually five, is$ (1) $\frac{1}{3}$ (2) $\frac{1}{10}$ (3) $\frac{13}{20}$ (4) $\frac{3}{13}$ 452. $If 6 is the mean of a Poisson distribution, then P (X \geq 3) =$ (1) $1 - \frac{25}{e ^{6}}$ (2) $e^{- 6} - 25$ (3) $24 - 25 e^{6}$ (4) $e^{- 3}$ 453. $A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = 1, 2, 3, 4, 5, 6, 7 and reports that it is even. The probability that it is actually even is$ (1) $\frac{2}{5}$ (2) $\frac{1}{10}$ (3) $\frac{1}{5}$ (4) $\frac{3}{5}$ 454. $A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X \geq 5 ∣ X > 2) is :$ (1) $\frac{125}{216}$ (2) $\frac{11}{36}$ (3) $\frac{5}{6}$ (4) $\frac{25}{36}$ 455. $Suppose A and B are events of a random experiment such that P (A) = \frac{1}{3}, P (A \cap B) = \frac{1}{5} and P (A \cup B) = \frac{3}{5} . Then, match the items of List-I with the items of List-II List-I: A. P (A ∣ B) B. P (B^{'}) C. P (A \cap B^{'}) D. P (B \cap A^{'}) List-II: (i) \frac{2}{15} (ii) \frac{4}{15} (iii) \frac{8}{15} (iv) \frac{2}{3} (v) \frac{3}{7}$ (1) $(iv) (i) (ii) (iii)$ (2) $(v) (i) (ii) (iii)$ (3) $(iv) (ii) (i) (v)$ (4) $(v) (iii) (i) (ii)$ 456. $Two events A and B are such that P (A) = \frac{1}{4}, P (A / B) = \frac{1}{4} and P (B / A) = \frac{1}{2} . Consider the following statements : (I) P (A^{'} / B^{'}) = \frac{3}{4} (II) A and B are mutually exclusive (III) P (A / B) + P (A / B^{'}) = 1 Then,$ (1) $only (I) is correct$ (2) $only (I) and (II) are correct$ (3) $only (I) and (III) are correct$ (4) $only (II) and (III) are correct$ 457. $A bag contains 6 red, 2 white and 8 blue balls. Three are drawn at random from the bag. Match the items of List-I with those items of List-II. List-I (A)Probability that none of the balls is white (B) Probability of getting 2 white and 1 blue ball (C) Probability of getting 2 blue and 1 white ball (D) Probability of getting 1 red, 1 white and 1 blue ball List-II (P) \frac{1}{70} (Q) \frac{6}{35} (R) \frac{13}{20} (S) \frac{1}{10} The correct match is A B C D$ (1) $(R) (P) (S) (Q)$ (2) $(R) (S) (T) (Q)$ (3) $(S) (R) (P) (T)$ (4) $(Q) (P) (T) (S)$ 458. $A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ^{2} is the variance of X, then 100 σ^{2} is equal to$