Probability Question?

Question

Hey, this is the question:

In a family of 6 children, what is the probability that exactly 1 child is female, assuming that P(male)=P(female)?

The choices are:

(1) 32/64; (2) 7/64; (3) 6/64, (4) 58/64

Can someone please explain how to get the answer?

Answer 1

the answer is 1.

if P=P then its an equal number. so it would be half male half female. in number one that fraction can be reduced to 1/2..see?  

Answer 2

in case it does  not matter WHICH child is female, then:

there are 6 children, so we can have: 1 child female, 2 females, 3 females, 4 females, 5 females or 6 females.

these are all the cases.

so 6 posibile cases.

P( exactly 1 child is female) = the right choise / total no of choises = 1 / 6.

so i guess none of the possible answers is right.

that's if my judgement is correct :)

Answer 3

Each child can be male or female.  So the total number of families is 2^6 = 64.  Now exactly 6 of these have just one female.  So the answer is 6/64.

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