A club with 31 members is voting on a proposal A group of 5

A club with 31 members is voting on a proposal. A group of 5 has decided to vote in favor of the proposal while each of the rest of the members vote independently with a chance of 49% in favor of the proposal. What are the chances that the proposal will get the majority vote.

Solution

A club with 31 members is voting on a proposal. A group of 5 has decided to vote in favor of the proposal while each of the rest of the members vote independently with a chance of 49% in favor of the proposal. What are the chances that the proposal will get the majority vote.

To get majority vote we need 16

But 5 decided to vote

So, out of remaining 26 we need minimum 11 votes

n=26

p=0.49

Expectation = np = 12.74

Variance = np(1 - p) = 6.4974

Standard deviation = 2.549

P( x >=11) = p( z > (11-12.74)/2.549) = p(z> -0.68) = 0.7517

The required P= 0.7517