Answer:
The probability is [tex]P(X \ge 10 ) = 0.558 [/tex]
Step-by-step explanation:
From the question we are told that
The probability of making a successful save is p = 0.80
The sample size n = 12
Generally the distribution of number of saves made by the lacrosse goalie follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^r * (1- p)^{n-r}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the probability that the lacrosse goalie will make at least 10 saves
is mathematically represented as
[tex]P(X \ge 10 ) = P(X = 10 ) + P(X = 11 ) + P(X = 12)[/tex]
=>[tex]P(X \ge 10 ) = [ ^{12}C_{10} * (0.80)^{10} * (1- 0.80)^{12-10}] + [ ^{12}C_{11} * (0.80)^{11} * (1- 0.80)^{12-11}] + [ ^{12}C_{12} * (0.80)^{12} * (1- 0.80)^{12-12}] [/tex]
=>[tex]P(X \ge 10 ) = [ 66 * 0.1073 * 0.04] + [ 12 * 0.0859 * 0.2] + [1* 0.0687} * 1] [/tex]
=>[tex]P(X \ge 10 ) = 0.558 [/tex]
