Or and AND Problems

• Or problems
  • P(A or B) = P(A) + P(B) - P(A and B)
  • These involve a single operation.
  • Usually involve the word or
  • But two events.
  • Examples:
    • A die is rolled, what is the probability that it is a 6 or even?
    • A card is selected what is the probability that it is a face card or a heart?
    • A card is selected, what is the probability that it is a queen or a club?
    • A card is selected, what is the probability that it is an ace or a jack?
  • In the last case, since both events can not occur at the same time, they are called mutually exclusive
• AND problems.
  • P(A and B) = P(A) × P(B)
  • The event is composed of two different operations.
  • Frequently do not involve the word and.
  • Examples:
    • A die is rolled twice, what is the probability both results are 2.
    • Two cards are selects (without replacement) what is the probability that both are kings?
    • Two cards are selects (with replacement) what is the probability that both are kings?
  • Event A and event B are independent events if the occurrence of either event in no way affects the probability of occurrence of the other event.
  • In the three examples above, which are independent events and which are dependent?
• A student has a 5 question multiple choice exam. Each question has four answers. If the student picks answers at random find the probability
  • That any question is right.
  • That only the first question is right.
  • All five questions are right.
  • None of the questions are right.
  • At least one question is right.