Question

sams 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?
a. ( p(bcup s)=0.69 )
b. ( p(bcup s)=0.27 )
c. ( p(bcup s)=0.33 )
d. ( p(bcup s)=0.8 )

Explanation:

Step1: Calculate total number of shirts

Total shirts \(n = 8 + 7=15\)

Step2: Calculate number of blue or striped shirts

Number of blue shirts \(n(B)=8\), number of striped shirts \(n(S)=5 + 4=9\), number of blue - and - striped shirts \(n(B\cap S)=5\)
Using the formula \(P(B\cup S)=\frac{n(B)+n(S)-n(B\cap S)}{n}\)
Substitute values: \(n(B) = 8\), \(n(S)=9\), \(n(B\cap S)=5\), \(n = 15\)
\(P(B\cup S)=\frac{8 + 9-5}{15}=\frac{12}{15}=0.8\)

Answer:

D. \(P(B\cup S)=0.8\)