Question

Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts. Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the probability that Sam randomly chooses a shirt that is blue or has stripes?

Answer 1

The answer is 80%.

Explanation:

B = the event that the shirt is blue,

G = the event that the shirt is green

and

S = the event that the shirt is striped.

So, n(B) = 8, n(G) = 7, n(B and S) = 5, n(G and S) = 4.

n(S) = 5 + 4 = 9.

We have

Therefore, the required probability is

Thus, the answer is 80%.

Answer 2

Answer: The answer is 80%.

Step-by-step explanation: Let us define the following events.

B = the event that the shirt is blue,

G = the event that the shirt is green

and

S = the event that the shirt is striped.

So, n(B) = 8, n(G) = 7, n(B and S) = 5, n(G and S) = 4.

n(S) = 5 + 4 = 9.

We have

`n(B\cup S)=n(B)+n(S)-n(B\cap S)=8+9-5=12.`

Therefore, the required probability is

`p=(n(B\cup S))/(8+7)=(12)/(15)=(4)/(5)=0.8=80\%.`

Thus, the answer is 80%.