Question

An orange tabby cat has a litter of 8 kittens. If the probability is 0.38 that an orange tabby kitten will be female, what is the probability that exactly three of the eight will be male

Answer 1

The probability is
`P(X = 3) =  0.10575`

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

`p = 1 -  q`

=>
`p = 1 -  0.38`

=>
`p =0.62`

Generally the distribution of kitten follows a binomial distribution

i.e

`X  \~ \ \ \  B(n , p)`

and the probability distribution function for binomial distribution is

`P(X = r) =  ^(n)C_r *  p^r *  (1- p)^(n-r)`

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

`P(X = 3) =  ^(8)C_3 *  (0.62)^3 *  (1- 0.62)^( 8- 3)`

=>
`P(X = 3) =  56 *  (0.62)^3 *  (1- 0.62)^( 8- 3)`

=>
`P(X = 3) =  0.10575`