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Mutually Exclusive Events (disjoint)

Mutually Exclusive Events (disjoint). Events A and B are mutually exclusive when only one can happen. . A. B. nine. Ace. Events are Not Mutually Exclusive . Two events can occur at the same time. Red. Ace. Both red and an ace. Multiplication Rule for INDEPENDENT Events.

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Mutually Exclusive Events (disjoint)

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  1. Mutually Exclusive Events (disjoint) Events A and B are mutually exclusive when only one can happen. A B nine Ace

  2. Events are Not Mutually Exclusive Two events can occur at the same time. Red Ace Both red and an ace

  3. Multiplication Rule for INDEPENDENT Events Multiplication Rule for DEPENDENT Events Probability that both A and B occur Probability of A happening overall Probability of B happening given that A has happened

  4. CLICK IN YOUR ANSWER What is the probability of picking a king and queen from a deck of cards (if you replace the card after you pick)? If you are rolling three dice, what is the probability that all three show a number less than 5? Of the 13 pitchers on the Orioles, 5 are left-handers and 8 right-handers. If 2 pitchers are selected at random, what is the probability that at least one of them is right-hander? P(at least one is right handed) = 1 – P(none are right) P(at least one is right handed) = 1 – (5/13)(4/12) P(at least one is right handed) = 1 – 0.13 = 0.87=87%

  5. We have a standard deck of 52 cards. What’s the probability of pulling out two aces in a row? Example 1 continued • P(A1 AND A2) = P(A1)P(A2|A1) P(A1) = 4/52 • There are now 3 aces left in a 51-card pack P(A2|A1) = 3/51 • Overall: P(A1 AND A2) = (4/52) (3/51) = .0045

  6. Compliments: the probability the event does not occurwritten as: P(Ac) or P(A’) Compliment Rule: P(A) = 1– P(Ac) Example: What is the probability of not rolling doubles? P(not rolling doubles) = 1 – P(doubles) = 1 – 6/36 = 30/36 = 83%

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