A doctor tells a woman that she will have twin boys Twins ar

A doctor tells a woman that she will have twin boys. Twins are either \"identical\" or \"fraternal.\" For the purposes of this problem, let\'s assume that 1/3 of twins are identical (NOTE: identical twins must be of the same sex; fraternal twins need not be). Assume that identical twins are equally likely to be both boys or both girls, while for fraternal twins all possibilities are equally likely.

(a) What is the probability that the woman\'s twin boys are identical?

Solution

P(identical | twin boys)

P(twin boys) = P(frat twin boys) + P(identical twin boys)

P(twin boys) = (2/3)(1/3) + (1/3)(1/2)

2/9 + 1/6

4/18 + 3/18

7/18

Now, P(identical twin boys) = 1/6

So, P(identical | twin boys) = 1/6 / (7/18)

1/6 * 18/7

3/7 --> ANSWER