Question

You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

Answer 1

Complete Question:

You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

a. What is the probability that the first 3 shirts are button-downs when you replace each shirt before choosing the next one?

b. What is the probability that the first 3 shirts are button-downs when you do not replace each shirt before choosing the next one?

Answer:

a) Probability of selecting 3 button down shirts with replacement = 0.064

b) Probability of selecting three button down shirts without replacement = 0.033

Explanation:

The total number of shirts = 3 t shirts + 3 polo shirts + 4 button - downs

The total number of shirts = 10

a) Three button down shirts are selected with replacement

Number of button down shirts available = 4

Probability of selecting a button down shirt = 4/10 = 0.4

Probability of selecting 3 button down shirts with replacement = 0.4 * 0.4 * 0.4 = 0.064

b) Probability of selecting three button down shirts without replacement

Probability of selecting the first button down shirt = 4/10 = 0.4

Probability of selecting the second button down shirt = 3/9 = 0.33

Probability of selecting the third button down shirt = 2/8 = 0.25

Probability of selecting three button down shirts without replacement = 0.4 * 0.33 * 0.25 = 0.033

Answer 2

a) P = 64/1000 = 0.064

b) P = 1/30 = 0.033

Completed question:

You are packing clothes for vacation and don't want to take any button-down shirts. You randomly choose 3 shirts from a drawer containing 3 t-shirts, 3 polo shirts, and 4 button-downs. (put both answers in as a reduced fraction)

a. What is the probability that the first 3 shirts are button-downs when you replace each shirt before choosing the next one?

b. What is the probability that the first 3 shirts are button-downs when you do not replace each shirt before choosing the next one?

Explanation:

Given;

Number of T-shirts = 3

Number of Polo shirts = 3

Number of button-downs = 4

Total number of shirts = 3+3+4 = 10

Number of shirts to be selected = 3

a) with replacement

probability P that the first 3 shirts are button-downs is;

P = 4/10 × 4/10 × 4/10

P = 64/1000 = 0.064

b) without replacement

probability P that the first 3 shirts are button-downs is;

P = 4/10 × 3/9 × 2/8

P = 24/720 = 1/30

P = 1/30 = 0.033