Question

question
if ( a ) and ( b ) are independent events with ( p(a) = 0.60 ) and ( p(a \text{ and } b) = 0.30 ), find ( p(b) ).
give your answer as a percent, rounded to two decimal places if necessary.
provide your answer below:
□%

Explanation:

Step1: Recall the formula for independent events

For independent events \( A \) and \( B \), the probability of their intersection is given by \( P(A \text{ AND } B) = P(A) \times P(B) \).

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

We know \( P(A) = 0.60 \) and \( P(A \text{ AND } B) = 0.30 \). Substitute these values into the formula:
\( 0.30 = 0.60 \times P(B) \)
To find \( P(B) \), divide both sides by \( 0.60 \):
\( P(B) = \frac{0.30}{0.60} = 0.5 \)

Step3: Convert to a percentage

To convert \( 0.5 \) to a percentage, multiply by \( 100 \):
\( 0.5 \times 100 = 50.00\% \)

Answer:

\( 50.00\% \)