Q. 3.65 - A First Course in Probability

Question

Assume, as in Example $3h$, that percent of twins are of the same sex. Given that a newborn set of twins is of the same sex, what is the conditional probability that the twins are identical? 

Step-by-Step Solution

Answer

The conditional probability of twins being identical supplied they are of the same sex, $P(I\mid SS)=0.4375$.

Step 1: Given Information

The data given in the example are given below. The probability of twins being identical, $P\left(I\right)=0.28$

Probability of the twins being of the same sex, $P(S S)=0.64$

Step 2: Assumption of the problem

The assumption made by the statistician conducting the experiment is that if the twins are identical, then they are of the same sex. This means that the probability of twins being of the same sex given that they are identical,

$P(\mathrm{SS}\mid \mathrm{I})=1$

Step 3: Finding the conditional probability

The problem deals with finding the conditional probability of twins being identical provided they are of the same sex, $P(I\mid SS)$

Applying Bayes theorem,

$P(I\mid SS)=\frac{P(SS\mid I)\times P\left(I\right)}{P\left(SS\right)}$

$=\frac{1\times 0.28}{0.64}$

We get,

$=0.4375$.

Step 4: Final Answer

The conditional probability of twins being identical provided they are of the same sex, $P(I\mid SS)=0.4375$.