Algebra > Probability

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Match List-I with List-II if $P(A) = \frac{3}{7}$, $P(B) = \frac{4}{7}$ and $P(A \cup B) = \frac{5}{7}$ | List-I | List-II | | :--- | :--- | | (A) $P(A \cap B)$ | (I) $\dfrac{2}{3}$ | | (B) $P(A \mid B)$ | (II) $\dfrac{5}{7}$ | | (C) $P(B \mid A)$ | (III) $\dfrac{1}{2}$ | | (D) $P(A' \cup B')$ | (IV) $\dfrac{2}{7}$ | Choose the correct answer from the options given below:

(A) - (III), (B) - (IV), (C) - (I), (D) - (II)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

(A) - (II), (B) - (IV), (C) - (I), (D) - (III)

✅ Correct Option: 3

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It is given that 3% of items manufactured by an industry are defective. The probability that a packet of 250 items contains one defective item is: [Given: $e^{-7.5} \approx 0.000553$ ]

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Let X denotes the number of doublets obtained in 3 throws of a pair of dice.

Match List-I with List-II

List-I	List-II
(A) $P(X = 0)$	(I) $\frac{1}{216}$
(B) $P(X = 1)$	(II) $\frac{15}{216}$
(C) $P(X = 2)$	(III) $\frac{75}{216}$
(D) $P(X = 3)$	(IV) $\frac{125}{216}$

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2025: 3 June Shift 1

Which of the following statements are correct?

(A) The mean and variance of the Poisson distribution are equal.

(B) The mean and variance of a Binomial distribution are equal.

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(D) If the variance of a Poisson distribution is 2, then P(X = 2) = $2e^{-2}$

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2026: 22nd May Shift 2

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2025: 21 May Shift 2

If $X$ is a random variable which can assume values $0, 1, 2, 3$ or $4$ such that $P(X = 1) = P(X = 2)$ and $3P(X = 3) = 4P(X = 4) = P(X = 0) = \frac{1}{8}$ , then $P(X > 0)$ is:

2025: 16 May Shift 1

In a game, a man wins ₹ 8 for getting a number greater than 3 and loses ₹ 3 otherwise, when a fair die is thrown. The man decided to throw a die 4 times but to quit as and when he gets a number greater than 3. If X denotes the amount which the man wins or loses, then which of the following are correct?

(A) All the possible values of X are 8, 5, 2 and -1.

(B) The probability distribution of X is:

X	8	5	2	-1	-12
P(X)	1/2	1/4	1/8	1/16	1/16

(D) The variance of X is 6615/256.

Choose the correct answer from the options given below:

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