Question

One card is drawn at random from a deck of 52 cards. The first card is not replaced, and a second card is drawn. (Enter your probabilities as fractions.)

(a) Find the probability that both cards are hearts.



(b) Find the probability that the first card is a spade and the second is a club.

Answer 1

The probability of choosing a heart, P(Heart) = 13/52 = 0.25.

Without replacement, you now have 51 cards left in the deck.

So the probability of subsequently choosing a Spade is, P(Spade) = 13/51.

The probability of choosing a heart AND then a space, without replacement is:
(13/52) * (13/51) = .06372549

(Remember, "AND" statements envoke the multiplication rule; "OR" statements envoke the additional rule. And when you sample WITH replacement, you have to then account for the missing cards in subsequent draws.)