Consider selecting one card at a time from a 52card deck Not

Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck of

cards)

If the card selection is without replacement, what is the probability that the first card is an ace and

the second card is also an ace? (Express the answer in simplest fraction form)

If the card selection is with replacement, what is the probability that the first card is an ace and

the second card is also an ace? (Express the answer in simplest fraction form)

Solution

a)
Drawing a 2 card from the deck withOut Replacement = 52 C 2
Drawing an Ace card, we have 4 Ace card in a pack of 52, Two card drawn is Ace = 4 C 2
probability that the first card is an ace and the second card is also an ace = 4 C 2 / 52 C 2 = 12/2652 = 1/221 = 0.00452

b)
Drawing a 2 card from the deck with Replacement = 52 C 1 * 52 C 1
Drawing an Ace card, we have 4 Ace card in a pack of 52, First card drawn is Ace = 4 C 1 and the Second drawn Ace card is also 4 C 1. becuase First drawn cars is replaced to Deck
probability that the first card is an ace and the second card is also an ace = 4 C 1 * 4 C 1 / 52 C 1 * 52 C 1 = 16 / (52)^2 = 16 / 2704 = 1/169 = 0.005917