Suppose hat two beams called the Hogs and the Grunts are in a playoff series whe
ID: 3221058 • Letter: S
Question
Suppose hat two beams called the Hogs and the Grunts are in a playoff series where the first team to win 2 games the series. For each game they play, the probability that the Hogs 0.56 and the probability the Grunts win is 0.44. (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 why)? (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? Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to win 3 games wins the series. For each game they play, the probability that the Bears win is 0.53 and the probability the wildcats win is 0.47 (a) What is the probability that the Bears win the series in exactly 3 games(i.e. only 3 games are required to finish the series and the Bears are the ones that win)? (b) What is the probability that the Wildcats win the series in exactly 3 games? (c) What is the probability that the Bears win the series in exactly games? d) What is the probability that the Wildcats win the series in exactly 4 games? (e) What is the probability that the Bears win the series in exactly 5 games? (f) What is the probability that the Wildcats win the series in exactly 5 games? (g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care how many games are required)? (h) What is the probability that the Wildcats win the series?Explanation / Answer
Hogs and Grunts
Here there will be maximum 3 games will be played. Also, as there is no infomation about tie is given hence we consider either of the player will win the game.
Probability that Hog wins, p = 0.56
Probability that Grunt wins, q = 0.44
(A)
Probability that Hogs win series in exactly 2 games = p^2 = 0.56^2 = 0.3136
(B)
Probability that Grunts win the series in exactly 2 games = q^2 = 0.44^2 = 0.1936
(C)
Probability that Hogs win the series in exactly 3 games = p*q*p + q*p*p
= 0.56*0.44 * 0.56 + 0.44 * 0.56 * 0.56
= 0.276
(D)
Probability that Grunts win the series in exactly 3 games = q*p*q + p*q*q
= 0.44 * 0.56 * 0.44 + 0.56 * 0.44 * 0.44
= 0.217
(E)
Probability that Hogs win the series = p^2 + p*q*p + q*p*p
=0.56^2 + 0.56 * 0.44*0.56 + 0.44 * 0.56 * 0.56
= 0.589
(F)
Probability that Grunts win the series = q^2 + q*p*q + p*q*q
= 0.44^2 + 0.44 * 0.56 * 0.44 + 056 * 0.44*0.44
= 0.410