Answer:
a) P=0.185
b) P=0.608
c) P=0.593
Step-by-step explanation:
The question is not complete
<em>"In an NBA championship series, the team that wins four games out of seven is the winner. Suppose that teams A and B face each other in the championship games and that team A has a probability 0.55 of winning a game over team B.</em>
<em>a. What is the probability that team A will win the series in 6 games?</em>
<em>b. What is the probability that team A will win the series?</em>
<em>c. If teams A and B were facing each other in a regional playoff series, which is decided by winning three out of 5 games, what is the probability that team A would win the series?
</em>
a) It is implicit that 6 games are played. The number of games needed to win a series in 6 games is 4, and the last winning should be in the 6th game.
So we have 5 random results in the first 5 games in which A team wins 3 matches and losses 2 matches.
This can be modeled as a binomial distribution with k=3, n=5 and p=0.55.

Then, this probability has to be multiplied by the probability of winning the last game.

The probability that team A will win the series in 6 games is P=0.185.
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b) In this case, we have to calculate the probability of A winning at least 4 games. When a team reaches 4 wins, the series is over. This can happen in 4, 5, 6 or 7 games.
The probability of winning the series is:
![P(W)=[P(3;3)+P(3;4)+P(3;5)+P(3;6)]*P(win\,last\,game)](https://tex.z-dn.net/?f=P%28W%29%3D%5BP%283%3B3%29%2BP%283%3B4%29%2BP%283%3B5%29%2BP%283%3B6%29%5D%2AP%28win%5C%2Clast%5C%2Cgame%29)
Probability of 3 wins in 3 games

Probability of 3 wins in 4 games

Probability of 3 wins in 5 games

Probability of 3 wins in 6 games

Then
![P(W)=[P(3;3)+P(3;4)+P(3;5)+P(3;6)]*P(win\,last\,game)\\\\P(W)=[0.166+0.299+0.337+0.303]*0.55=1.105*0.55=0.608](https://tex.z-dn.net/?f=P%28W%29%3D%5BP%283%3B3%29%2BP%283%3B4%29%2BP%283%3B5%29%2BP%283%3B6%29%5D%2AP%28win%5C%2Clast%5C%2Cgame%29%5C%5C%5C%5CP%28W%29%3D%5B0.166%2B0.299%2B0.337%2B0.303%5D%2A0.55%3D1.105%2A0.55%3D0.608)
The probability of team A of winning the series is P=0.608.
c) The probabilty of winning the regional playoff is
![P(W)=[P(2;2)+P(2;3)+P(2;4)]*P(win\,last\,game)](https://tex.z-dn.net/?f=P%28W%29%3D%5BP%282%3B2%29%2BP%282%3B3%29%2BP%282%3B4%29%5D%2AP%28win%5C%2Clast%5C%2Cgame%29)

Then,
![P(W)=[P(2;2)+P(2;3)+P(2;4)]*P(win\,last\,game)\\\\P(W)=[0.303+0.408+0.368]*0.55=1.079*0.55=0.593](https://tex.z-dn.net/?f=P%28W%29%3D%5BP%282%3B2%29%2BP%282%3B3%29%2BP%282%3B4%29%5D%2AP%28win%5C%2Clast%5C%2Cgame%29%5C%5C%5C%5CP%28W%29%3D%5B0.303%2B0.408%2B0.368%5D%2A0.55%3D1.079%2A0.55%3D0.593)