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

Explanation:

Step1: Define Events and Total

Let \( B \) be blue shirts, \( S \) be striped shirts. Total shirts: \( 8 + 7 = 15 \). \( P(B)=\frac{8}{15} \), \( P(S)=\frac{5 + 4}{15}=\frac{9}{15} \), \( P(B\cap S)=\frac{5}{15} \).

Step2: Apply Union Formula

Use \( P(B\cup S)=P(B)+P(S)-P(B\cap S) \). Substitute: \( \frac{8}{15}+\frac{9}{15}-\frac{5}{15}=\frac{12}{15}=0.8 \)? Wait, no—wait, 8 + 9 - 5 = 12? Wait 8 (blue) + 9 (striped) - 5 (blue and striped) = 12. 12/15 = 0.8? Wait but let's recalculate: total shirts 15. Blue:8, Striped:5+4=9, Blue and Striped:5. So \( P(B\cup S)=\frac{8 + 9 - 5}{15}=\frac{12}{15}=0.8 \). Wait but option C is 0.8. Wait but let me check again. 8 blue, 7 green. Striped blue:5, striped green:4. So total striped:9. So blue or striped: blue (8) + striped green (4) = 12. 12/15 = 0.8. Yes, so \( P(B\cup S)=0.8 \), which is option C.

Answer:

C. \( \boldsymbol{\text{P}(B \cup S) = 0.8} \)