Question

two events, a and b, are independent of each other. $p(a)=\frac{1}{6}$ and $p(a \text{ and } b)=\frac{1}{8}$. what is $p(b)$ written as a decimal? round to the nearest hundredth, if necessary.\
0.02\
0.04\
0.29\
0.75

Explanation:

Step1: Recall independence formula

For independent events, \( P(A \text{ and } B) = P(A) \times P(B) \).

Step2: Solve for \( P(B) \)

Rearrange the formula: \( P(B) = \frac{P(A \text{ and } B)}{P(A)} \). Substitute \( P(A)=\frac{1}{6} \) and \( P(A \text{ and } B)=\frac{1}{8} \): \( P(B)=\frac{\frac{1}{8}}{\frac{1}{6}}=\frac{1}{8} \times \frac{6}{1}=\frac{6}{8}=0.75 \).

Answer:

0.75