math help please!?

Question

Find the probability that a family of 6 children will have only 1 boy.

please try to use pascal's triangle to show me how you got your answer

Answer 1

I will try to explain this

when you build pascal's triangle you would have this

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1

and the sum of the entries in the last line is 64 (1+6+15+20+15+6+1=64)

so 64 is the total number of possible outcomes

so now you have to find how many have just one boy

that would be this

BGGGGG, GBGGGG, GGBGGG, GGGBGG, GGGGBG and GGGGGB

there are six possible outcomes of birth where there is only 1 boy

so then you would have 6/64=9.38%

Answer 2

basically you do 1/2^6 and will get 1/64.