Math 3081 Fall 2017 You can work in groups of up to 3 people, the group will han

Question

Math 3081 Fall 2017 You can work in groups of up to 3 people, the group will hand in one solution set. NOTE: Write out all your steps in a clear manner. 1. (3 pts) If P(A)-4, P(B)6, and P(C)-5, find P(A UBUC) if A, B, and C are independent. 2. A bucket has three marbles: two black and one white. You will continuously draw marbles from the bucket until you get a white, but if you draw a black you put it along with another black and a white marble back in the bucket. If we let X number of draws: a) (4 pts) find a formula for P(X-k). b) (3 pts) set up ECX). Extra Credit (3 pts): get this number (you have to show work to get full credit) 3. For the probability mass function /(z)-x(+ 1) fr z = 1, 2, 3, 4, 5 a) (3 pts) find c b) (2 pts) find ECX) 4. Randomly choose a number, X, where fx (a) r S 5. If X 6). b) (3 pts) Find P(Y-2 W>6). 5. For the probability density function()E for 1 S s9 a) (4 pts) find vt b) (3 pts) find P(x -4)2 > 4) c) (4 pts) find ECX). 6. A game of baseball will be played by tossing a fair coin (a toss will be a 'pitch). A head will count as a strike and a tail will be a ball. The coin will be tossed until there is either an 'out' or a 'walk where an out occurs if there are three srikes before there are four balls, while it's a walk otherwise. a) (2 pts) Find P(set an out in three pitches) b) (3 pts) Find P(out) c) (4 pts) Using the P(out) from part (b), find P(0 runs in a half of an 'inning') (a half of an inning ends when there are three outs, a team will score 1 run if there are exactly four walks before the third out, 2 runs if there are exactly five walks before the third out, ...therefore a team will score 0 runs if they get three or fewer walks in an inning). d) (3 pts) again using P(out) from (b), find a formula for P(k runs). e) (4 pts) Find the probability that a team scores more than 2 runs in 3 half innings. Extra Credit (3 pts) If X-number of runs by one team in a half of an inning, find E(X). Sh ouw aiul

Explanation / Answer

1.

P(A B C) = P(A) + P(B) + P(C) P(A B) P(A C) P(B C) + P(A B C).

= P(A) + P(B) + P(C) - P(A)*P(B) - P(B)*P(C) - P(A)*P(C) + P(A)*P(B)*P(C)

= .4 +.6 + .5 - .4*.6-.6*.5-.5*.4 + .4*.6*.5

= 0.88

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