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)

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?

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

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

Step-by-step 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