Answer:
The probability is [tex]P(X = 3) = 0.10575 [/tex]
Step-by-step explanation:
From the question we are told that
The number of kittens n = 8
The probability that n orange tabby kitten will be female q = 0.38
Generally the probability that n orange tabby kitten will be male is mathematically represented as
[tex]p = 1 - q[/tex]
=> [tex]p = 1 - 0.38[/tex]
=> [tex]p =0.62[/tex]
Generally the distribution of kitten follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = r) = ^{n}C_r * 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
So
Generally the probability that exactly three of the eight will be male is mathematically represented as
[tex]P(X = 3) = ^{8}C_3 * (0.62)^3 * (1- 0.62)^{ 8- 3}[/tex]
=> [tex]P(X = 3) = 56 * (0.62)^3 * (1- 0.62)^{ 8- 3}[/tex]
=> [tex]P(X = 3) = 0.10575 [/tex]
