Respuesta :
Answer:
The probability that A wins the series is:
[tex]P(x=3) = \frac{n!}{(n-3)!3!}(2p)^{3}(1-2p)^{n-3}[/tex]
Step-by-step explanation:
Since team A and B are playing a series of games, let n be the total number of games played. Since there is a probability that either A or B will win if any of the two teams wins three games, then this experiment follows a binomial distribution. Binomial, because the experiment(i.e games played) is carried out n number of times.
Now, if the probability that team B wins the series is p, then the probability that team A wins the series is 2p(from the question).
Since our aim is to know the probability of A winning the series, then the probability of success is 2p and probability of failure is 1-2p
The probability density function for binomial distribution is given as:
[tex]P(x) = \frac{n!}{(n-x)!x!}p^{x}q^{n-x}[/tex]
Where:
n = total number of trials
x = total number of successes
p = probability of success
q = probability of failure
Therefore, we have, after substituting:
[tex]P(x=3) = \frac{n!}{(n-3)!3!}(2p)^{3}(1-2p)^{n-3}[/tex]
Which is the required answer.
