I want to be promoted to Vice President of my Organization F

I want to be promoted to Vice President of my Organization. For this to happen, I must get the votes of each of A, B, and C, and I must get two or more of the votes of D, E, and F. If the chance that I get the votes of A, B, C, D, E, and F are respectively .4, .5, .6, .7, .8 and .9, find the chance that I am promoted.

Solution

We add up the probabilities of the possibilities so that you will win. These are

P(win) = P(A,B,C,D,E) + P(A,B,C,E,F) + P(A,B,C,D,F) + P(A,B,C,D,E,F)

= 0.4*0.5*0.6*0.7*0.8 + 0.4*0.5*0.6*0.8*0.9 + 0.4*0.5*0.6*0.7*0.9 + 0.4*0.5*0.6*0.7*0.8*0.9

= 0.28968 [ANSWER]