There are 20 passengers on the plane. Assume that any gender combination of the passengers is equally likely. What is the probability that there will be at least on woman on the plane?

Question

anonymous · Answer

why is that?

anonymous · Answer

flip a coin 20 times, what is the likelihood that you will flip at least one heads? much more than 1/20

anonymous · Answer

im so confused!

anonymous · Answer

Going with the coin flip analogy, there is only one outcome that has all tails.  all the rest have at least one heads.  so, how many combinations were there?

anonymous · Answer

oh now i get it..goodness when i mess things like this up ik its time for bed...

anonymous · Answer

I get a ridiculous answer, so I am needing a check: 1048575/1048576

zarkon · Answer

that is correct

anonymous · Answer

ok

anonymous · Answer

which is (2^20-1)/(2^20) = 1048575/1048576

zarkon · Answer

P(at lest on F)=1-P(all M)

=1-P(m1 and M2 and ... and M20)
=1-P(m1)*P(m2)*...*P(M20)

$$=1-\frac{1}{2}\times\frac{1}{2}\times\cdots\times\frac{1}{2}=1-\frac{1}{2^{20}}=\frac{2^{20}-1}{2^{20}}$$

as already stated.

zarkon · Answer

*at least