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. $p(b cup s) = 0.83$ b. $p(b cup s) = 0.27$ c. $p(b cup s) = 0.69$ d. $p(b cup s) = 0.8$

Explanation:

Step1: Calculate total shirts

Total = Blue + Green = $8 + 7 = 15$

Step2: Define events and values

Let $B$ = blue shirt, $S$ = striped shirt.
$P(B) = \frac{8}{15}$, $P(S) = \frac{5+4}{15} = \frac{9}{15}$, $P(B \cap S) = \frac{5}{15}$

Step3: Apply addition rule

Use $P(B \cup S) = P(B) + P(S) - P(B \cap S)$
$\frac{8}{15} + \frac{9}{15} - \frac{5}{15} = \frac{12}{15} = 0.8$

Answer:

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