Answer to Question #228581 in Statistics and Probability for Talha

Question

If 60% of the voters in a large district prefer candidate A, What is probability that in a sample of 12 voters exactly 7 will prefer A.

can you explain this question please.?

Answer 1

Let $X=$ the number of voters in a sample of 12 voters who will prefer A: $X\sim Bin(n, p).$

Given $n=12, p=0.6, q=1-p=0.4.$

$$P(X=7)=\dbinom{12}{7}(0.6)^7(0.4)^{12-7}$$

$$=792(0.6)^7(0.4)^{5}=0.227030335488\approx0.22703$$