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Two cards are picked at random from a pack of 52 playing cards, one at a time wi...


Question

Two cards are picked at random from a pack of 52 playing cards, one at a time with replacement. What is the probability that the two cards are both spades and both hearts?

Options

A) 8/169

B) 1/16

C) 1/8

D) 1/32

The correct answer is B.

Explanation:

In a pack of playing cards, total no of cards
= 52 (excluding jokers)
No of Hearts = 13
No of Spades = 13
No of Clubs = 13
No of Diamonds = 13
Pr(2 Spades) = \(\cfrac{1}{4} \times \cfrac{1}{4}\)
\(= \cfrac{1}{16}\) (with replacement)
Pr(2 Spades) = \(\cfrac{1}{4} \times \cfrac{1}{4} = \cfrac{1}{16}\)

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Discussion (2)

  • Steven Jekwu

    The correct answer is C.
    P(2Spades)= 1/4 × 1/4
    =1/16
    P(2Hearts)=1/4 × 1/4
    =1/16
    P(2Spades) + P(2Hearts)= 1/16 + 1/16
    =1/8

  • In a pack of playing cards, total no of cards
    = 52 (excluding jokers)
    No of Hearts = 13
    No of Spades = 13
    No of Clubs = 13
    No of Diamonds = 13
    Pr(2 Spades) = \(\cfrac{1}{4} \times \cfrac{1}{4}\)
    \(= \cfrac{1}{16}\) (with replacement)
    Pr(2 Spades) = \(\cfrac{1}{4} \times \cfrac{1}{4} = \cfrac{1}{16}\)

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