Answer to Question #298539 in Statistics and Probability for om singh

Question

In a certain town, 40% of the eligible voters prefer candidate

A, 10% prefer candidate B, and the remaining 50% have no

preference. You randomly sample 10 eligible voters. What is

the probability that 4 will prefer candidate A, 1 will prefer

candidate B, and the remaining 5 will have no preference?

Answer 1

Solution:

Here we are given that P(A) = 0.4, P(B) = 0.1 and P(nil ) 0.5

Also n = 10 is the sample size

a) Probability that 4 prefers A, 1 prefer B and 5 will have no preference is computed as:

$=^5C_4(0.4)^4 \times ^6C_1(0.1)\times(0.5)^5=0.0024$

Therefore 0.0024 is the required probability here.