Conditional Probability and Bayes' Theorem — Engineering Board Exam Practice Questions

10 free engineering board exam reviewer questions on Conditional Probability and Bayes' Theorem (Combinatorics and Probability), each with the correct answer and a worked solution.

  1. A family has two children. Given that at least one of them is a boy, what is the probability that both are boys?
  2. Two cards are dealt from a standard deck. Given that at least one of them is an ace, what is the probability that both are aces?
  3. A disease affects 2% of a population. A test detects the disease in 95% of those who have it, but also gives a false positive for 10% of…
  4. Given P(A)=0.5, P(B A)=0.4, and P(B A')=0.2, find P(B).
  5. Bag 1 has 3 red and 2 blue balls and bag 2 has 1 red and 4 blue balls. A bag is chosen at random and one ball is drawn from it. What is…
  6. Machine A makes 60% of a factory's items and 2% of its items are defective. Machine B makes the other 40% and 5% of its items are…
  7. A box has 4 red and 6 blue balls. Two balls are drawn without replacement. Given that the first is red, what is the probability that the…
  8. Two fair dice are rolled and the sum is 8. What is the probability that at least one die shows a 3?
  9. A card is drawn from a standard deck and is known to be a face card (jack, queen, or king). What is the probability that it is a king?
  10. If P(A B)=0.12 and P(B)=0.4, find P(A B).