A 2001 preseason NCAA football poll asked respondents to answer the question, \"

Question

A 2001 preseason NCAA football poll asked respondents to answer the question, "Will the Big Ten or the Pac-10 have a team in this year's national championship game, the Rose Bowl?" Of the 13,429 respondents, 2961 said the Big Ten would, 4494 said the Pac-10 would, and 6823 said neither the Big Ten nor the Pac-10 would have a team in the Rose Bowl (www.yahoo.com, August 30, 2001).

What is the probability that a respondent said neither the Big Ten nor the Pac-10 will have a team in the Rose Bowl (to 2 decimals)?

What is the probability that a respondent said either the Big Ten or the Pac-10 will have a team in the Rose Bowl (to 2 decimals)?

Find the probability that a respondent said both the Big Ten and the Pac-10 would have a team in the Rose Bowl (to 2 decimals).

Explanation / Answer

Let

B = said Big 10 will make it
P = said Pac10 would make it

a)

P(B U P)' = 6823/13429 = 0.508079529 [ANSWER]

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b)

P(B U P) = 1 - P(B U P)' = 0.491920471 [ANSWER]

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c)

P(B n P) = P(B) + P(P) - P(B U P)

= 2961/13429 + 4494/13429 - 0.491920471

= 0.063221386 [ANSWER]

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