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 the formula for independent events

For two independent events \( A \) and \( B \), the probability of both \( A \) and \( B \) occurring is given by \( P(A \text{ and } B) = P(A) \times P(B) \).

Step2: Substitute the known values into the formula

We know that \( P(A) = \frac{1}{6} \) and \( P(A \text{ and } B) = \frac{1}{8} \). Substituting these into the formula, we get:
\[
\frac{1}{8} = \frac{1}{6} \times P(B)
\]

Step3: Solve for \( P(B) \)

To solve for \( P(B) \), we can rearrange the equation by multiplying both sides by \( 6 \) and then dividing by \( 1 \) (or simply multiplying both sides by \( 6 \)):
\[
P(B) = \frac{1}{8} \div \frac{1}{6} = \frac{1}{8} \times \frac{6}{1} = \frac{6}{8} = \frac{3}{4}
\]

Step4: Convert the fraction to a decimal

\( \frac{3}{4} = 0.75 \)

Answer:

0.75