Section 6.4 F ind Probabilities of Compound Events
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Transcript of Section 6.4 F ind Probabilities of Compound Events
Section 6.4Find Probabilities of Compound Events
Compound Event: A compound event combines two or more events, using the word "AND" or the word "OR".
Mutually Exclusive Events: Events with no common outcomes
Overlapping Events: Events with at least one common outcome
Independent Events: The occurrence of one event has no effect on the occurrence of the other
Dependent events: The occurrence of one event affects the occurrence of the other
Conditional probability: If A and B are dependent events, then the probability that event B will occur given that event A has occurred is called the conditional probability of B given A.
Example 1Find the probability of A OR BYou randomly choose a card from a standard deck of 52 playing cards.
a.Find the probability that you choose a 9 or a King.
Are these events overlapping or mutually exclusive?P(9 or King) = P(9) + P(King)
b. Find the probability that you choose an Ace or a spade. Are these events overlapping or mutually exclusive?
P(Ace or spade) = P(Ace) + P(spade) - P(Ace and spade)
Example 2Find the probability of A AND BYou roll two number cubes (dice). What is the probability that you roll a 1 first and a 2 second? Are these events dependent or independent?
P(1 and 2) = P(1) x P(2)
Example 3Find the probability of A and B
A box contains 8 red markers and 3 blue markers. You choose one marker at random, do not replace it, then choose a second marker at random. What is the probability that both markers are blue? Are these events dependent or independent?