Question

What is the probability that the second card is an ace, given that the first card is a king? (b) What is the probability that the second card is an ace, aiven that the first card is an ace? What is the probability that the second card is (c) spade, given that the first card is a spade? (d) Suppose two cards are drawn at random from the deck with replacement. What is the probability that the second card is a spade, given that the first card is a spade?

Answer 1

a) Number of aces remaining after the first king is taken = 4

Number of cards remaining in the deck = 52 - 1 = 51

P(second card is an ace | first card is a king) = 4/51

b) Number of aces remaining after the first ace is taken = 4 - 1 = 3

Number of cards remaining in the deck = 52 - 1 = 51

P(second card is an ace | first card is an ace) = 3/51

c) Number of spades = 13

Number of spades remaining after the first spade is taken = 13 - 1 = 12

Number of cards remaining in the deck = 52 - 1 = 51

P(second card is a spade | first card is a spade) = 12/51

d) When cards are drawn with replacement

Number of spades remaining after the first spade is taken and replaced = 13

Number of cards remaining in the deck = 52

P(second card is a spade | first card is a spade) = 13/52

= 1/4