11 Suppose the probability that a US resident has traveled t

11. Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09,

and to both countries is 0.04. Now suppose three U.S. residents are selected at random.

a) What’s the probability that all three U.S. residents have visited Canada?

b) What’s the probability that at least one of them has visited Canada?

c) What’s the probability that exactly one of the selected U.S. residents has visited Canada?

12.The “Archers”, uses a 2-quarterback system. Peyton is the quarterback for 40% of the plays,

Eli is the quarterback for the other 60%. Neither quarterback is perfect. Peyton throws an

interception 16% of the time. Eli throws an interception 12% of the time he is in the game.

a) Create a Tree Diagram for this situation in the space above.

b) What is the probability that Peyton is in the game and throws an interception?

c) What percent of the time does an Archer quarterback throw an interception?

d) You go to the other room to refill your non-alcoholic beverage. While you are there

your friends shout “The Archers have just thrown another interception.”

Given this information, who was more likely to have thrown the interception? ______

Are you surprised by this answer? Why, or, why not?

Support your answer with two conditional probabilities.

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11. Suppose the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09,

and to both countries is 0.04. Now suppose three U.S. residents are selected at random.

a) What’s the probability that all three U.S. residents have visited Canada?

P(3 ) = 0.18*0.18*0.18 = 0.005832

b) What’s the probability that at least one of them has visited Canada?

P( x > 1) = 0.18 + 0.18*0.18 + 0.18*0.18*0.18 = 0.218232

c) What’s the probability that exactly one of the selected U.S. residents has visited Canada?

P( x=1) = 0.18