5. After many years of happy marriage, Mrs Abdey announces 'I have three children'. (a) Mrs Abdey then says at least two of them are boys. Use Bayes' theorem to determine the probability that all three of her children are boys. (b) Mrs Abdey then says the two oldest children are boys. Use Bayes' theorem to determine the probability that all three of her children are boys. You may assume that the probability of a birth resulting in a boy is 0.5, and hence also for a girl. You may also assume that the sex of each child is independent. Note you are explicitly asked to use Bayes' theorem to solve this