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(b ∪ s) = 0.27
b. p(b ∪ s) = 0.8
c. p(b ∪ s) = 0.69
d. p(b ∪ s) = 0.33

Explanation:

Step1: Calculate total number of shirts

Total number of shirts = 8 (blue) + 7 (green)=15.

Step2: Define events and use probability formula

Let \(B\) be the event of choosing a blue - shirt and \(S\) be the event of choosing a striped - shirt.
The formula for \(P(B\cup S)=P(B)+P(S)-P(B\cap S)\).
Number of blue shirts \(n(B) = 8\), so \(P(B)=\frac{8}{15}\).
Number of striped shirts \(n(S)=5 + 4=9\), so \(P(S)=\frac{9}{15}\).
Number of blue and striped shirts \(n(B\cap S)=5\), so \(P(B\cap S)=\frac{5}{15}\).

Step3: Substitute values into the formula

\[

$$\begin{align*} P(B\cup S)&=\frac{8}{15}+\frac{9}{15}-\frac{5}{15}\\ &=\frac{8 + 9-5}{15}\\ &=\frac{12}{15}\\ & = 0.8 \end{align*}$$

\]

Answer:

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