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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?

A) 8/169

B) 1/16

C) 1/8

D) 1/32

### Explanation:

In a pack of playing cards, total no of cards
= 52 (excluding jokers)
No of Hearts = 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) = $$\cfrac{1}{4} \times \cfrac{1}{4} = \cfrac{1}{16}$$

## Discussion (2)

• Steven Jekwu

=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 Clubs = 13
No of Diamonds = 13
Pr(2 Spades) = $$\cfrac{1}{4} \times \cfrac{1}{4}$$
$$= \cfrac{1}{16}$$ (with replacement)
Pr(2 Spades) = $$\cfrac{1}{4} \times \cfrac{1}{4} = \cfrac{1}{16}$$