Probability Question?

Question

A given school in a certain state has 3 mathematics teachers. The probability in that state that a mathematics teacher is female is 0.4. In the same state the probability that a mathematics teacher is a graduate is 0.7. What is the probability that in the given school none of the three mathematics teachers is a female graduate? 
The answer is 0.373 and I'm not sure how to get it.

Answer 1

Probability of mathmatics teacher is a female ,q = 0.4

Probability of mathmatics teacher is a male ,p = 1 - q =1-0.4 =0.6

Calculate probabilities:

P(all of male) =3c0 p^3

                    =1(0.6)^3

                    =0.216

P(2 males, 1 female) =3c1 p^2 q

                               =3(0.6)^2(0.4)

                                =0.432

 

P(1 males, 2 female) =3c2 p q^2

                               =3(0.6)(0.4)^2

                                =0.288

 

P(3 females)               =3c3q^1

                               =(0.4)^3

                                =0.064

Find the probability that in the given school none of the three mathematics teachers is a female graduate:

P(no female graduate) = P(all of male)+(1-0.7)(P(2 males, 1 female))  

                                       +(1-0.7)^2(P(1 male, 2 females))+(1-0.7)^3(P(3 females))

                                 =0.216+0.3(0.432)+0.3^2(0.288)+0.3^3(0.064)

                                 = 0.216+0.1296+0.02592+0.001728

                                  = 0.3732