Question

Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities.

a) Assume the cards are drawn without replacement. Find the probability of drawing a club followed by a club.
b) Assume the cards are drawn with replacement. Find the probability of drawing a club followed by a club.
a. The probability of drawing a club followed by a club without replacement is
(Simplify your answer.)
b. The probability of drawing a club followed by a club with replacement is
(Simplify your answer.)

Answer 1

A.0.059 , B.0.063

Explanation:

1. There are 13 clubs in a pack of 52 cards;

Hence the probability of picking the first club is 13/52;

The probability of picking the second is 12/ 51( remember one card has been removed already so the total number of cards decreases).

Probability of picking two clubs in succession is ;

13/52 × 12/51 = 0.0588 = 0.059( to the nearest thousandth).

2. The probability of drawing a club followed by a club with replacement is;

13/52 × 13 /52 = 0.0625 = 0.063( to the nearest thousandth)