Probability of getting two boys question

[Dell]

in a family with 2 children , what is the possibility that there will be 2 boys if we know that at least one is a boy,

the correct answer is 0.33 but how do i get it,


the way i see it we have 4 options
boy girl
girl boy
boy boy
girl girl

therefore only one is a boy- boy option, therefore p=0.25

 

[Dell]

i see my problem, the options are
boy girl
girl boy
boy boy

so it really is 1/3, but how do i get this using equations

using P(X/Y) etc

 

[HallsofIvy]

What you have done is a perfectly valid method and far easier than "using equations".