What are the odds?

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?

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.

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.

Start at the overlap and work your way out. Find what percent is left only in beards and only in mustaches.

What percent of men are accounted for according to our model? Add together the percents.

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.

*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.

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.