Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then Match the LIST-I with LIST-II, LIST-I, LIST-II, A. P(X=0), I. 1, B. P(X=1), II. 19/34, C. P(X=2), III. 13/34, D. P(X<3), IV. 1/17, Choose the correct answer from the options given below: Option 1: A-I, B-II, C-III, D-IV Option 2: A-II, B-III, C-IV, D-I Option 3: A-III, B-IV, C-I, D-II Option 4: A-IV, B-I, C-II, D-III

Answer: A-II, B-III, C-IV, D-I. Solution: With 522=1326 equally likely pairs: P(X=0) = 392/1326 = 19/34 (II). P(X=1) = 13x39/1326 = 13/34 (III). P(X=2) = 132/1326 = 1/17 (IV). Since X can only be 0,1,2, P(X<3)=1 (I).

Algebra

Probability

Medium

core

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. If X denotes the number of Spades in two draws, then

Match the LIST-I with LIST-II

LIST-I LIST-II
A. $P(X=0)$ I. 1
B. $P(X=1)$ II. $\dfrac{19}{34}$
C. $P(X=2)$ III. $\dfrac{13}{34}$
D. $P(X<3)$ IV. $\dfrac{1}{17}$

Choose the correct answer from the options given below:

LIST-I		LIST-II
A. $P(X=0)$		I. 1
B. $P(X=1)$		II. $\dfrac{19}{34}$
C. $P(X=2)$		III. $\dfrac{13}{34}$
D. $P(X<3)$		IV. $\dfrac{1}{17}$

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

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

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

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

✅ Correct Option: 2

With $\binom{52}{2}=1326$ equally likely pairs:

$P(X=0) = \binom{39}{2}/1326 = 19/34$ (II).

$P(X=1) = 13\times39/1326 = 13/34$ (III).

$P(X=2) = \binom{13}{2}/1326 = 1/17$ (IV).

Since $X$ can only be $0,1,2$ , $P(X<3)=1$ (I).

2025: 22 May Shift 1

Probability that a man speaks truth is $\frac{3}{4}$ . He throws a die and reports that it is a six. The probability that it is actually a six is

2026: 14 May Shift 2

A pair of coins thrown then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Probability of occurance of head on both coins is	I.	$\dfrac{3}{4}$
B.	Probability of occurance of at least one tail is	II.	$\dfrac{1}{2}$
C.	Probability of occurance of one tail only is	III.	$1$
D.	Probability of a tail appears on one coin given that only one coin shows head.	IV.	$\dfrac{1}{4}$

Choose the correct answer from the options given below:

2026: 22 May Shift 2

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals

2025: 15 May Shift 2

If a random variable $X$ has the following probability distribution:

X	0	1	2	3	4
P(X)	k	2k	3k	k²	6k²

, then

Match List-I with List-II

List-I	List-II
(A) k	(I) 3/7
(B) $P(X < 2)$	(II) 6/49
(C) $P(X > 3)$	(III) 1/7
(D) $P(2 \leq X \leq 3)$	(IV) 22/49

Choose the correct answer from the options given below:

2026: 30 May Shift 1

A company manufactured a product through 4 units. A, B, C and D. The probability that a product is manufactured are $\frac{3}{10},\frac{1}{5},\frac{1}{10}$ and $\frac{2}{5}$ by units A, B, C and D respectively. The probability that it will be defective are $\frac{1}{4},\frac{1}{3}$ and $\frac{1}{12}$ if it is produced by A, B, C respectively and there is no defective from unit D. A product is chosen, it is found to be defective.

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. The Probability that the defective product is from A	I. 4/9
B. The Probability that the defective product is from B	II. 0
C. Probability of defective product	III. 1/2
D. Probability that the defective product is from D	IV. 3/20

Choose the correct answer from the options given below:

2025: 2 June Shift 1

If the sum and difference of squares of mean and variance of a Binomial distribution is $\frac{225}{256}$ and $\frac{63}{256}$ respectively, the $P(X \geq 2)$ is:

Solution

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