Question

after studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. what is the probability that she will have identical twins? that is, find the probability of identical twins given that the twins consist of two boys.

Answer 1

Events

• A: the babies are identical twins

,

• B: the babies are two boys

We have to find the probability of identical twins given that the twins consist of two boys. This is expressed mathematically as P(A|B). This probability is computed as follows:

$P(A|B)=\frac{P(A\cap B)}{P(A)}$

From the previous question, P(A) = 5/11

P(A∩B) means the probability of A and B, that is, the babies are identical twins and two boys. From the table:

$\begin{gathered} P(A\cap B)=\frac{\text{ number of favorable outcomes}}{\text{ total possible outcomes}} \\ P(A\cap B)=\frac{10}{10+10+6+6+6+6} \\ P(A\cap B)=\frac{10}{44} \\ \text{ Simplifying:} \\ P(A\cap B)=\frac{2\cdot5}{2\cdot22}=\frac{5}{22} \end{gathered}$

Substituting P(A) = 5/11 and P(A∩B) = 5/22 into the formula, we get:

$\begin{gathered} P(A|B)=\frac{\frac{5}{22}}{\frac{5}{11}} \\ P(A|B)=\frac{5}{22}\cdot\frac{11}{5} \\ P(A|B)=\frac{11}{22} \\ \text{ Simplifying:} \\ P(A|B)=\frac{11}{2\cdot11} \\ P(A|B)=\frac{1}{2} \end{gathered}$

The probability is 1/2