Respuesta :
Answer:
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?
Step-by-step 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
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
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
