If 2 cards are selected from a standard deck of cards. The first card is placed back in the deck before the second card is drawn. Find the following probabilities: P(Heart and Club)

Answer 1

A deck of cards is made up of:

Hearts: A, 2, 3, 4, 5, 6 7, 8, 9, 10, J, Q, K (13 cards)

Clubs: A, 2, 3, 4, 5, 6 7, 8, 9, 10, J, Q, K (13 cards)

Diamonds: A, 2, 3, 4, 5, 6 7, 8, 9, 10, J, Q, K (13 cards)

Spades: A, 2, 3, 4, 5, 6 7, 8, 9, 10, J, Q, K (13 cards)

There are 13•4 or 52 total cards with 13 hearts when you make your first pick. Therefore the probability of getting a heart is 13/52 (or reduced down, 1/4)

Prior to drawing your second pick, it says you put your first card back in the deck. So now, for your second pick, there are 52 total cards with 13 clubs. Therefore the probability of getting a club is 13/52 (or reduced down, 1/4)

For BOTH events to happen, you multiply the two probabilities: 1/4 • 1/4 = 1/16 so the probability of picking a heart AND a club is 1/16