QA – Placement Quizzes | Probability | Question 14

Two cards are drawn together from a pack of 52 cards. What is the probability that one is a spade and one is a heart?
(A) 3/20

(B) 29/34

(C) 47/100

(D) 13/102

Answer: (D)

Explanation: Number of ways to draw 2 cards from a pack of 52 cards = ⁵²C₂ = 1326.
Number of ways to draw a spade from 13 spades = ¹³C₁ = 13.
Number of ways to draw a heart from 13 hearts = ¹³C₁ = 13.
Number of ways to draw a spade and a heart = 13 * 13 = 169.
Therefore, required probability = 169/1326 = 13/102.


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