Question

If A and B are independent events with P(A)=0.60 and P(A AND B)=0.30, find P(B).

Give your answer as a percent, rounded to two decimal places if necessary.

Answer 1

To find the probability of event B (P(B)), we use the formula for the probability of two independent events occurring together (P(A AND B) = P(A) × P(B)). Given the probabilities P(A)=0.60 and P(A AND B)=0.30, we find P(B) to be 50%.

Step-by-step explanation:

To find the probability of event B, we use the fact that events A and B are independent. The probability of two independent events occurring together, P(A AND B), is equal to the product of their probabilities: P(A) × P(B).

Given that:

• P(A) = 0.60
• P(A AND B) = 0.30

We can set up the equation:

P(A AND B) = P(A) × P(B)

Substituting the given values:

0.30 = 0.60 × P(B)

Dividing both sides by 0.60 gives us:

P(B) = 0.30 / 0.60

P(B) = 0.50

Converting the decimal to a percent:

P(B) = 50%

This process illustrates the determination of the probability of event B based on the independence of events A and B.