6. 12 points My Notes Ask Your Teacher Suppose that two teams called the Hogs an
ID: 3358593 • Letter: 6
Question
6. 12 points My Notes Ask Your Teacher Suppose that two teams called the Hogs and the Grunts are in a playoff series where the first team to win 2 games wins the series. For each game they play, the probability that the Hogs win is 0.54 and the probability the Grunts win is 0.46. (a) What is the probability that the Hogs win the series in exactly 2 games (i.e. only 2 games are required to finish the series and the Hogs are the ones that win)? (b) What is the probability that the Grunts win the series in exactly 2 games? (c) What is the probability that the Hogs win the series in exactly 3 games? (d) What is the probability that the Grunts win the series in exactly 3 games? (e) What is the probability that the Hogs win the series (i.e. the Hogs win but we don't care how many games are required)? (f) What is the probability that the Grunts win the series?Explanation / Answer
a)probability =P(Hogs wins both the games)=0.54*0.54=0.2916
b) probability =P(Grunts wins both the games)=0.46*0.46=0.2116
c)probability =P(Hog wins first then Grunts wins then Hog wins+grunts wins first then Hogs wins then Hog wins)
=0.54*0.46*0.54+0.46*0.54*0.54=0.268272
d)probability=P(Grunts wins first then Hog wins then Grunts wins+Hogs wins first then Grunts wins then Grunts wins) =0.46*0.54*0.46+0.54*0.46*0.46=0.228528
e) probability that Hogs wins the series=P(wins in 2 games +wins in 3games)=0.2916+0.268272=0.559872
f)probability=P(grunts wins)=P(wins in 2 game +wins in 3games)=0.2116+0.228528=0.440128
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