Question

In one town, 47% of all voters are Democrats. If three

voters are randomly selected for a survey, what is the
probability that they are all Democrats?

Answer 1

The probability that the all three votes are Democrats

P(X=3) = 0.1038

Explanation:

Step(i):-

Given that the all voters are democrats

The probability that the all voters are democrats

p = 47% =0.47

q = 1-p =1-0.47 = 0.53

Step(ii):-

Let 'X' be the random variable in binomial distribution

`P(X=r) = n_{C_(r) } p^(r) q^(n-r)`

The probability that the all three votes are Democrats

P(X=3) = 0.1038

n=3 and r=3

`P(X=3) = 3_{C_(3) } (0.47)^(3) (0.53)^(3-3)`

`P(X=3) = 1 (0.47)^(3)`

P(X=3) = 0.1038

Final answer:-

The probability that the all three votes are Democrats

P(X=3) = 0.1038