Question

In each of the 4 races, the democrats have 60% chance of winning.

Assuming that the races are independent of each other, what is the

probability that:

The Democrats will win a majority of the races.

Answer 1

Let $X=$ the number of wins of the Democrats out of 4 races:

X$\sim Bin(n,p)$

Given $n=4, p=0.60, q=1-p=0.40.$

$$P(X>2)=P(X=3)+P(X=4)$$

$$=\dbinom{4}{3}(0.6)^3(0.4)^{4-3}+\dbinom{4}{4}(0.6)^4(0.4)^{4-4}$$

$$=0.3456+0.1296=0.4752$$