probablity family has children that are all boys

[zarbolias1]

Assuming that boy and girl babies are equally likely, find the probablity that a family with four children has all boys given that the first two are boys.

I found that there could be bbgg, bbbg, bbbb.
So I thought that the chance of having all boys would be 1, this is not right. Please help.

 

[royhaas]

You left out bbgb. So there are 4 equiprobable events. Also, because of independence, the probability is the same as the probability of two boys in a row.