Draww a tree diagram to help me find the probability that thandi and richard will have:3sons,2sons1daugther,3childern of the same sex
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In the tree diagram above, 1, 2 and 3 represent 1st, 2nd and 3rd child. F=female, M=male.

In brackets on the leaves we have the permutation of children, showing all possibilities.

We exclude the possibility of twins, triplets, etc., and take the probability of a boy or girl to be the same=1/2.

The probability of 1/2 is shown on the branches or twigs. We move from left to right, multiplying the probabilities as we go until we reach the required leaf.

3 sons is MMM, and there is just one occurrence right at the top. So 1/2*1/2*1/2=1/8.

2 sons and 1 daughter is MMF, MFM or FMM=1/8+1/8+1/8=3/8.

3 children of same sex is MMM or FFF=1/8+1/8=1/4.

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