Mutually Exclusive and Independent Events — Engineering Board Exam Practice Questions

6 free engineering board exam reviewer questions on Mutually Exclusive and Independent Events (Combinatorics and Probability), each with the correct answer and a worked solution.

1. A single card is drawn from a deck. What is the probability that it is a heart or a spade? (These are mutually exclusive events.)
2. A bag has 5 red and 7 blue balls. A ball is drawn, replaced, then another is drawn. What is the probability that both are red? (These are…
3. The probability that event A occurs is 0.4 and event B occurs is 0.5. If A and B are independent, find the probability that both occur.
4. The probability of rain tomorrow is 0.3 and the probability of rain the day after is 0.4, and the two events are independent. Find the…
5. Events A and B are mutually exclusive with P(A)=0.3 and P(B)=0.25. Find P(A or B).
6. A student estimates a 0.6 probability of passing Math and a 0.7 probability of passing English, and the two events are independent. Find…