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

Answer:

The  probability that the all three votes are  Democrats

P(X=3) = 0.1038

Step-by-step 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