Events A and B are dependent events. The probability
that event A occurs is 20%. The probability that events A and B both
occur is 8%. What is the probability that event B occurs given that
event A occurs? Explain how you found your answer.
To find the probability that event B occurs given that event A occurs, we can use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
Given that the probability that event A occurs is 20% (or 0.20) and the probability that both events A and B occur is 8% (or 0.08), we can substitute these values into the formula:
P(B|A) = 0.08 / 0.20
Simplifying this equation, we get:
P(B|A) = 0.4
Therefore, the probability that event B occurs given that event A occurs is 40% (or 0.40).
To find the probability that event B occurs given that event A occurs, we will use the concept of conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. In this case, we want to find the probability that event B occurs, given that event A has occurred.
The formula to calculate conditional probability is:
P(B|A) = P(A and B) / P(A)
We are given that the probability that event A occurs is 20% (or 0.20) and the probability that events A and B both occur is 8% (or 0.08).
Plugging these values into the formula, we can calculate the probability of event B occurring given that event A has occurred:
P(B|A) = 0.08 / 0.20
Simplifying this, we get:
P(B|A) = 0.4
Therefore, the probability that event B occurs given that event A occurs is 0.4 or 40%.