Question

7. No Broken Hearts [2.5 Points]Robert has a standard deck of 52 playing cards. Robert shuffles the deck, draws a card, andchecks if the card has a suit of hearts. If the card has a suit of hearts he stops. Otherwise,he replaces the card back into the deck and continues to repeat this process until he drawsa card that has a suit of hearts.a) What is the probability that Robert performs exactly 5 draws

Answer 1

0.079

Explanation:

Number of suit of hearts = 13

Total number of cards in deck = 52

P(drawing a suit of heart) = number of suit of heart / total number of cards in deck

P(drawing a suit of heart) = 13 /52 = 1 /4

Hence, Probability of success, p = 1/4

P(not drawing a suit of heart) = 1 - 1/4 = 3/4

Hence, Probability of performing exactly 5 draws :

To perform exactly 5 draws :

1st draw = not a heart suit

2nd draw = not a heart suit

3rd draw = not a heart suit

4th draw = not a heart suit

5 draw = a heart suit

P(performing exactly 5 draws) =

(3/4 * 3/4 * 3/4 * 3/4 * 1/4)

= 0.0791015625

= 0.079