Question

In the US, 50.8% of the people are female. Suppose that 10 people in the US were chosen at random. Find the probability that 6 of those people are female.

Answer 1

Given:

The female percentage is 50.8%

That is,

`P=0.508`

The number of people was chosen at random, n = 10.

To find: The probability that 6 of those people are female.

Step-by-step explanation:

Let us take,

`x=6`

Using the binomial distribution,

`P(X=x)=^nC_xP^x(1-P)^(n-x)`

On substitution we get,

`\begin{gathered} P(X=6)=^(10)C_6(0.508)^6(1-0.508)^(10-6) \\ =(10!)/((10-6)!6!)(0.508)^6(0.492)^4 \\ =(6!*7*8*9*10)/(1*2*3*4*6!)(0.508)^6(0.492)^4 \\ =7*3*10*(0.508)^6(0.492)^4 \\ =0.2115 \end{gathered}`

Hence, the probability that 6 of those people are female is 0.2115.

Final answer: 0.2115.