Question

In a recent school election at a large school we know that 45% of the students supported candidate X and the other 55% supported candidate Y. Assume everyone has a strong opinion about one candidate or the other. If we select 2 students at random what is the probability that they both supported the same candidate?

Answer 1

0.5050

Explanation:

Given that in a recent school election at a large school we know that 45% of the students supported candidate X and the other 55% supported candidate Y.

We know that each candidate is independent of other

Hence prob for supporting X = 0.45 for each student and y = 0.55

We select 2 students at random

The prob that they both supported the same candidate

=Prob both supported X or prob both supported Y

=prob both supported X + prob both supported Y(since mutually exclusive)

=
`(0.45)^2 +(0.55)^2\\=0.2025+0.3025\\=0.5050`