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.
This is conditional probability
Prob(B given A)
= P(B | A)
= P( A and B)/P(A)
= .08/.2
= .....
To find the probability of event B occurring 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 0.2), and the probability that both events A and B occur is 8% (or 0.08), we can substitute these values into the formula to find P(B|A):
P(B|A) = 0.08 / 0.2
Simplifying the expression:
P(B|A) = 0.4
Therefore, the probability that event B occurs given that event A occurs is 40% (or 0.4).
To explain how this answer was obtained, we used the definition of conditional probability. The probability of event B occurring given that event A occurs is equal to the probability of both events A and B occurring divided by the probability of event A occurring. By plugging in the provided probabilities for these events, we calculated the probability of event B given event A.