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.
How are these two (sentence and question) different?
The probability that events A and B both occur is 8%.
What is the probability that event B occurs given that event A occurs?
To find the probability that event B occurs given that event A occurs, we need to use the concept of conditional probability. The conditional probability of event B given event A is denoted as P(B|A).
The formula for conditional probability is:
P(B|A) = P(A and B) / P(A)
Given that events A and B are dependent, we are given that the probability of event A occurring is 20% (or 0.20), and the probability of events A and B both occurring is 8% (or 0.08).
Now, we can substitute these values into the formula to find the probability of event B given that event A occurs:
P(B|A) = 0.08 / 0.20 = 0.4
Therefore, the probability that event B occurs given that event A occurs is 0.4, or 40%.
Explanation of how the answer was found:
To find the conditional probability, we used the formula P(B|A) = P(A and B) / P(A) which states that the probability of event B given that event A has occurred is equal to the probability of both events A and B occurring divided by the probability of event A occurring.
We were given that the probability of event A occurring is 20% (0.20) and the probability of events A and B both occurring is 8% (0.08). By substituting these values into the formula, we found that the probability of event B occurring given that event A occurs is 40% (0.4).