Question

The following exercise refers to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck. If you put the first card back in the deck before you draw the next, what is the probability that the first card is a club and the second card is a spade? (Enter your probability as a fraction.)

Answer 1

Draw 1: Club

Number of Clubs = 13

Number of cards other than Clubs = 49

Total cards = 52

So,

P(Draw 1: Club) = 13/52 = 1/4

Draw 2: Spade

Number of Spades = 13

Number of cards other than Spades = 49

Total cards = 52

So,

P(Draw 2: Spade) = 13/52 = 1/4

So,

the probability that the first card is a club and the second card is a spade = 1/4 X 1/4 = 1/16

So,

Answer is:

1/16