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

Solution:- If we select 2 students at random what is the probability that they both supported the same candidate is 0.505.

P(X) = 0.45, P(Y) = 0.55

There are two ways of supported the same candidate i.e either both are supporting X or Y

P(Same) = P(X = 2) + P(Y = 2)

P(X) = 0.45,

x = 2, n =2

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(X = 2) = 0.2025

P(Y) = 0.55,

x = 2, n = 2

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(Y = 2) = 0.3025

P(Same) = P(X = 2) + P(Y = 2)

P(Same) = 0.2025 + 0.3025

P(Same) = 0.505