Question

if ( p(\text{not yellow})=\frac{4}{15} ), which best describes the probability of the complement of the event?
( p(\text{not yellow})=\frac{8}{15} )
( p(\text{not yellow})=\frac{11}{15} )
( p(\text{yellow})=\frac{8}{15} )
( p(\text{yellow})=\frac{11}{15} )

Explanation:

Step1: Recall the formula for complementary events

The formula for complementary events is \(P(A)+P(\text{not }A) = 1\). Let \(A\) be the event of getting yellow. Then \(P(\text{yellow})+P(\text{not yellow})=1\).

Step2: Solve for \(P(\text{yellow})\)

If \(P(\text{not yellow})=\frac{4}{15}\), then \(P(\text{yellow})=1 - P(\text{not yellow})\). Substitute the value of \(P(\text{not yellow})\) into the formula: \(P(\text{yellow})=1-\frac{4}{15}\). Calculate \(1=\frac{15}{15}\), so \(P(\text{yellow})=\frac{15 - 4}{15}=\frac{11}{15}\).

Answer:

\(P(\text{yellow})=\frac{11}{15}\)