Question

A deck of cards contains 52 cards. They are divided into four suits: spades, diamonds, clubs and hearts. Each suit has 13 cards: ace through 10, and three picture cards: Jack, Queen, and King. Two suits are red in color: hearts and diamonds. Two suits are black in color: clubs and spades.

Use this information to compute the probabilities asked for below and leave them in fraction form. All events are in the context that three cards are dealt from a well-shuffled deck without replacement.

a. The first and second cards are both hearts.
b. The third card is an eight.
c. None of the three cards is an ace.

Answer 1

a) P(first and second cards are both hearts) = P(first card is heart) x P(second card is heart) x P(any card)

= 13/52 x 12/51 x 1

= 1/17

b) P(the third card is an eight) = Number of favorable outcomes/Total number of outcomes

= 4/52 (There are four cards that have value 8)

= 1/13

c) P(none of the three cards is an ace) = P(first is not an ace) x P(second is not an ace) x P(third is not an ace)

= 48/52 x 47/51 x 46/50

= 4324/5525