In an NBA (National Basketball Association) championship series, the team who wins four [3]
games out. of seven will be the winner. Suppose that team A has probability 0.55 of winning
over team B and both teams A and B face each other in the championship games.
(a) What is the probability that team A will win the series in six games?
(b) What is the probability that team A will win the series?
(c) If both teams face each other in a regional playoff series and the winner is decided by
winning three out of five games, what is the probability that team A will win a playoff?
Answers
Given : In an NBA (National Basketball Association) championship series, the team who wins four games out. of seven will be the winner.
that team A has probability 0.55 of winning over team B
To Find :(a) What is the probability that team A will win the series in six games?
(b) What is the probability that team A will win the series?
(c) If both teams face each other in a regional playoff series and the winner is decided by
winning three out of five games, what is the probability that team A will win a playoff?
Solution:
P(A) winning p = 0.55
q = 1- 0.55 = 0.45
probability that team A will win the series in six games
Hence 6th game has to be won by team A
and in first 5 games 3 games has to be won by A
⁵C₃(0.55)³(0.45)²(0.55)
What is the probability that team A will win the series
in 4 matches , 5 matches , 6 matches , 7 matches
(0.55)⁴ + ⁴C₃(0.55)³(0.45)¹(0.55) + ⁵C₃(0.55)³(0.45)²(0.55) + ⁶C₃(0.55)³(0.45)³(0.55)
team A will win in 3 matches 4 matches , 5 matches
(0.55)³ + ³C₂(0.55)²(0.45)¹(0.55) + ⁴C₂(0.55)²(0.45)²(0.55)
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