A basketball game does not end in a tie. This means that it is either the team wins the game or they draw the game. These outcomes are independent becuase winning one game has no effect on the outcome of the next game. This means that we have a binomial distribution here. the formula for binomial distribution is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the number of trials
x is the number of successess
p is the probability of success
q is the probability of failure
We are concerned with the outcome of winning. This means that success is when the team wins. Thus,
p = 4/7
q = 1 - p = 1 - 4/7 = 3/7
n = 15
x = 8
We want to find P(x = 8)
By applying the binomial distribution formula,
P(x = 8) = 15C8 * (4/7)^8 * (3/7)^(15 - 8)
P(x = 8) = 6435 * (4/7)^8 * (3/7)^7
P(x = 8) = 0.194
The probability that in a season of 15 games they will win exactly 8 games is
0.194