cheat sheet STAT

# cheat sheet STAT - Bayes theorem A team consisting of three...

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Bayes theorem A team consisting of three boys and four girls must be formed from a group of nine boys and eight girls. If two of the girls are feuding and refuse to play on the same team, how many possibilities do we have? Sol 1 C(8 4)*C(9 3) - C(6 2)*C(9 3)=4620 Sol2 C(6 4)*C(9 3) + 2*( C(6 3)*C(9 3) ) For three events A;B;C, let A and B be independent, and C((-B . Find P(A((-B ((-C), when P(A) = 0.5, P(B) = 0.3 and P(C) = 0.01. Also find P(A U B U C), when P(C) = 0.2. Sol AUBUC =AUB (C((-B) P(AUBUC)=P(A)+P(B)-P(A(|)B)=P(A)+P(B)-P(A)*P(B)=0.5+0.3-0.5*0.3=.65 Suppose that 12 married couples take part in a contest. If 12 persons each win a prize, what is the probability that one from each couple is a winner. Sol (2^120 / C(24 12) To travel to Bangalore, India from State College, you need to change airplanes in Cincinnati, Atlanta, Paris and Mumbai. Suppose the pieces of luggage are lost independently at each of these airports. Suppose the chance of losing each piece of luggage at Paris airport is 4% and it is 5% at each of the other airports. If you are traveling with one piece of luggage in the baggage compartment,
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