Or and And problems

• Or problems involve a single experiment with multiple outcomes.
  • They usually involves the word "or"
  • A single die is tossed, what is the probability that a one or two is rolled.
  • A card is drawn from a standard deck, what is the probability that an ace or a two is drawn.
  • Remember A and B are sets: n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
  • so: P(A or B) = P(A) + P(B) - P(A and B)
• And problems involve two experiments
  • The word "and" is sometimes present, but sometimes it is implied.
  • It is the two different experiments that make it an and problem.
  • P(A and B) = P(A)× P(B)
  • Two cards are drawn from a standard deck, what is the probability that both are a queen?
  • A die is rolled twice, what is the probability that the sum is 12.
• Two events are mutually exclusive if it is impossible for both events to occur simultaneously.
  • Drawing both a red card and a black card when drawing a single card.
  • Rolling both an even number and a odd number on a single roll of the die.
• Two events are independent if the occurrence of either event in no way affects the probability of the occurrence of the other event.
  • The result of two different die rolls are independent.
  • Drawing two cards from a deck are dependent.
• If an experiment is performed with replacement the set of outcomes is returned to the original condition.
• If an experiment is performed without replacement the outcome selected is removed from the set of outcomes.
• Think drawing a card from a deck, or a name from a hat
• The P(an event happening at least once) = 1-P(event does not happen)
• Do problems page 724.