6. A game of baseball will be played by tossing a fair coin (a toss will be a \'

Question

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 strikes before there are four balls, while it's a walk otherwise. a) (2 pts) Find P(get an out in three pitches) b) (3 pts) Find P(out) c) (4 pts) Using the P(out) from part (b), find P(O 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 uising 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).

Explanation / Answer

a) P(get out in 3 pitches) = P(gettig 3 consecutive heads) = 0.5*0.5*0.5 = 0.125

b) P(out) = P(ever getting 3 consecutive heads, before 4 consecutive tails)

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