Question

if ( a ) and ( b ) are independent events with ( p(a) = 0.20 ) and ( p(a \text{ and } b) = 0.12 ), find ( p(b) ). give your answer as a percentage, rounded to two decimal places if necessary. provide your answer below:

Explanation:

Step1: Recall the multiplication rule for independent events

For independent events \( A \) and \( B \), the multiplication rule is \( P(A \text{ AND } B) = P(A) \times P(B) \).

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

We know \( P(A) = 0.20 \) and \( P(A \text{ AND } B) = 0.12 \). Rearranging the formula from Step 1 to solve for \( P(B) \), we get \( P(B)=\frac{P(A \text{ AND } B)}{P(A)} \). Substituting the given values, we have \( P(B)=\frac{0.12}{0.20} \).

Step3: Calculate the value and convert to percentage

First, calculate \( \frac{0.12}{0.20} = 0.6 \). To convert this to a percentage, multiply by 100: \( 0.6\times100 = 60\% \).

Answer:

\( 60.00\% \)