show work please A club with 27 members is voting on a propo

show work please

A club with 27 members is voting on a proposal. A group of 4 has decided to vote in favor of the proposal while each of the rest of the members vote independently with a chance of 40% in favor of the proposal. What are the chances that the proposal will get the majority vote.

Solution

P(k)=(27 C k) (0.42^k) (0.58^(27-k)) where (27 C k) = 27!/[(k)! * (27-k)!].
Therefore, to find the probability that the proposal is going to pass, we have:
P(proposal passing)=P(12)+P(13)+P(14)+P(15)+P(16)+P...