Please explain formulas used. Beyonce is having twins! Twins come in two differe
ID: 2934522 • Letter: P
Question
Please explain formulas used.
Beyonce is having twins! Twins come in two different types: identical or fraternal. Identical
twins are alike genetically (including gender) and are typically very similar in appearance.
Fraternal twins are genetically distinct and are not necessarily of the same gender. Suppose
there is a 30% chance the Beyonce will have identical twins and that each child is a boy or a
girl with equal probability, independently.
(a) Find the probability that Beyonce has one boy and one girl.
(b) Given that Beyonce has two boys, what is the probability that they are fraternal twins?
Explanation / Answer
a) Here we are given that there is a 30% chance that beyonce will have identical twins, also in case of identical twins as the gender has to be same, we cannot have one boy and one girl.
In case of fraternal twins which are going to happen with a probability of 0.7, the probability of having a boy and a girl would be given as:
= 2*0.5*0.5 because we could have two cases either BG or GB.
= 0.5
Therefore the probability that Beyonce has one boy and one girl, is computed as:
= Probability that Beyonce has fraternal twins * Probability that beyonce has one girl and one boy given that she has fraternal twins
= 0.7*(0.5) = 0.35
Therefore 0.35 is the required probability here.
b) Probability that beyonce has two boys is first computed as:
= Probability that she has identical twins * Probability that she has two boys given that she has identical twins +
Probability that she has fraternal twins * Probability that she has two boys given that she has fraternal twins
= 0.3*0.5 + 0.7*0.5*0.5
= 0.325
Now given that beyonce has two boys, probability that they are fraternal twins is computed as: ( Using Bayes theorem )
= Probability that she has fraternal twins * Probability that she has two boys given that she has fraternal twins / Probability that Beyonce has two boys
= 0.7*0.5*0.5 / 0.325
= 0.5385
Therefore 0.5385 is the required probability here.