Question

Assume 0.34 of all twin births are identical , and hence always have the same sex, while 0.66 are fraternal , and hence have the same sex 50% of the time. You learn that MIranda is expecting twins.

a, What is the probability that will have two girls?

b. You learned that Miranda gave birth to two girls. What is the probability that they are identical?

Answer 1

Solution:

Let I be the event that set of twins are from identical (monozygotic) birth.

let F be the event that twins are fraternal (dizygotic) and E be the event of having 2 girls as twins. A fraternal birth means birth from 2 different eggs and hence results into twins of same sex or of opposite sex with probability 0.5 each.

We have P(I)=0.34, P(F)=0.66,

P(E|I)=0.5 as identical leads to twins of same sex (boys and girls) which are equally likely.

P(E|F)=0.25 as fraternal leads to twins boys, girls and mixed with probabilities 0.25, 0.25 and 0.5 respectively.