Math 425: Practice problems for the first midterm exam

Advice: To better prepare for the exam, go over the "self-test problems and exercises" at the end of each chapter. Each of these has a complete solution in the back of the book.

  1. Suppose that in a deck of 20 cards, each card has one of the numbers 1, 2, 3, 4, 5, with four cards of each number. Ten cards are chosen from the deck at random.
  2. Two coins fall "heads up" with probabilities p1 and p2, respectively. Both coins are tossed.
  3. Consider two events A and B such that P(A)=0.3 and P(B)=0.4. Find the conditional probability P(A|B) under each of the following conditions:
  4. A parallel system functions whenever at least one of its components works. Consider a parallel system of 3 components and suppose that these components independently work with probabilities 0.7, 0.8, and 0.9.