And and OR Problems.

• Problems involving an or usually include the word or.
• They usually are a single action.
• A die is rolled, find the probability that the result is a 2 or a 3.
• Problems involving an and sometimes involve the word and.
• They usually are a multiple action
• Two cards are dealt from a deck of cards, find the probably that both are kings.
  • This could be rephrased as: find the probability that the first is a king and the second is a king.
• This doesn't mean that and will not show up in single action problems.
  • We just don't call these and problems. (in this book)
• For OR problems
  • $P(A \mbox{ or } B) = P(A) + P(B) - P(A\cap B)$
  • What does this formula remind you of?
  • $n(A\cup B) = n(A) + n(B) - n(A\cap B)$
  • That is because they are the same problem!
  • This is also written
  • $P(A \mbox{ or } B) = P(A) + P(B) - P(A \mbox{ and } B)$
  • A card is selected at random from a standard deck, find the probability that it is a king or a red card.
  • Two events are Mutually exclusive if it is impossible for both events to occur at the same time.
  • A card is selected at random from a standard deck, find the probability that it is a queen or a king.
• For AND problems
  • $P(A \mbox{ and } B) = P(A)\cdot P(B)$
  • Two cards are drawn from a deck of cards, find the probability both are kings.
• Two events are independent if the occurrence of either event in no way affects the probability of occurrence of the other event.
• If events are dependent, assume the first is successful when computing the probability of the second.
• Do some problems 23-28 and 29-36