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Dependent and Independent Events. What are the odds?. D ependent Events. To find the probability that a man has both a beard and a mustache would you multiply the probability of a man having a beard by the probability of a man having a mustache?. D ependent Events. No!
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Dependent and Independent Events What are the odds?
Dependent Events • To find the probability that a man has both a beard and a mustache would you multiply the probability of a man having a beard by the probability of a man having a mustache?
Dependent Events • No! • Men who have a beard are more likely to have a mustache than a man in general. Therefore men having a beard and men having a mustache are not mutually exclusive, or Dependent Events.
Dependent Events • Suppose 40% of men have beards, 35% have mustaches, and 30% of men have both a beard and a mustache. • What percent have neither a beard nor a mustache? • Make a Venn Diagram where there is some overlap.
Dependent Events • Start at the overlap and work your way out. • Find what percent is left only in beards and only in mustaches.
Dependent Events • What percent of men are accounted for according to our model? • Add together the percents.
Dependent Events • Since 45% of men have been accounted for based on our model, what percent of men are not accounted for? • 55% • That means that 55% of men have neither a beard nor a mustache.
Dependent Events • Suppose there are 3 brown socks, 5 pink socks, and 10 white socks in my drawer. If I reach in with out looking, what’s the probability I will get a pink sock? • 5 out of 13, , .345, or 34.5% chance.
Dependent Events • Assume I pull out a pink sock, and do not put it back in. What is the probability the second sock I pull out will also be a pink sock? • Think: There is one less pink sock and one less sock overall. • 4 out of 12, , .33, or 33% chance. • Since the first sock was not replaced the probability for the second sock is affected.
Independent Events • Think about rolling a die. Is it possible to roll two 5s in a row? • Yes! • This is because the first roll of the die has nothing to do with the second roll of the die. • The two rolls are called Independent Events. • p(A and B) = p(A) x p(B) • What’s the probability of rolling two 5 on two consecutive rolls? • or about 2.8%
Review Events *One of your classmates is selected at random. Let A represent the event that the person selected owns a computer, and B represent the event that the person selected owns an iPod. Are A and B mutually exclusive? Explain. *You are one of the ten finalists in a radio station contest for tickets to a concert. Names of the finalists are written on index cards, placed in a hat, and a name is randomly selected. Suppose that three sets of tickets are to be given away and that a single finalist can win only one set of tickets. Are the three events of selecting the three winners from the group of finalists independent events? Explain.
Review Events • You pick two cards from a standard deck of 52 cards. You replace the first card before picking the second. • a. Determine the probability that both cards are aces. • b. What is the probability that both cards are aces if the first card is not replaced before picking the second card? Compare your results to the probability in part a. • c. Determine the probability that the first card is a heart and the second card is a club. Assume the first card is not replaced before picking up the second card.
