Question

A drawer contains 3 tank tops, 6 short-sleeve shirts, 4 three-quarter sleeve shirts, and 5 long-sleeve shirts. What is the probability of randomly choosing a tank top and then a three-quarter sleeve length, if you replace the tank top?

A. 7/18
B. 1/27
C. 2/3
D. 1/18

Answer 1

I believe that the answer is 7/18, at least that’s what I got.

Answer 2

The probability of choosing a tank top and then a three-quarter sleeve length is:

1/27

Explanation:

The drawer contains:

3 tank tops, 6 short-sleeve shirts, 4 three-quarter sleeve shirts, and 5 long-sleeve shirts.

Now the drawing is done with replacement.

Hence, the drawing in the second chance is independent of drawing in the second chance.

Hence, we know that when two events A and B are independent then,

P(A∩B)=P(A)×P(B)

Hence,

P( choosing a tank top and then a three-quarter sleeve length) is:

P(choosing tank top)× P(choosing a three-quarter sleeve shirt)

= (3/18) × (4/18)

= 1/27

Hence, the probability is:

Option: B (1/27)