Question on Probability

Question

Suppose Erroll will pass his statistics test with probability 0.7, pass his fluid mechanics test with probability 0.5, and pass both with probability 0.37. What is the probability that Erroll will pass either the statistics or fluid mechanics test, but not both?

Answer 1

For this question, consider the event, "Erroll will pass his statistics test" as event "A". Consider the event "pass his fluid mechanics test" as event "B".

Therefore, P(A) = 0.7 and P(B) = 0.5. P(A and B) means the probability that Enroll will pass both his statistics test and his fluid mechanics test; therefore, P(A and B) = 0.37.

The probability that Erroll will pass either the statistics or fluid mechanics test in general, meaning the probability that Erroll will pass either the statistics or fluid mechanics test or both, is P(A or B).

In general, P(A or B) = P(A) + P(B) - P(A and B). Therefore, P(A or B) = 0.7 + 0.5 - 0.37 = 0,83. However, again, this probability also includes the probability that Erroll will pass both his statistics and fluid mechanics test. Since you do not want to include that probability, you will subtract P(A and B) from this general probability. Therefore, 0.83 - 0.37 = 0.46. This is your answer.

In the alternative, you could also take [P(A) - P(A and B)] + [P(B) - P(A and B)]. In this case, [0.7 - 0.37] + [0.5 - 0.37] = 0.33 + 0.13 = 0.46.