Question

In Exercises 25–32, find the probability and answer the questions. YSORT Gender Selection MicroSort’s YSORT gender selection technique is designed to increase the likelihood that a baby will be a boy. At one point before clinical trials of the YSORT gender selection technique were discontinued, 291 births consisted of 239 baby boys and 52 baby girls (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a boy born to a couple using MicroSort’s YSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a boy?

Short answer

The probability of a boy being born to a couple who have used the YSORT method is equal to 0.821.

Yes, the YSORT method is effective in increasing the probability of a boy being born.

Step-by-step solution

Given information

Out of 291 births, 239 boys and 52 girls were born with the help of a method known as the MicroSort’s YSORT.

Define the term probability

The probability of an event can be computed by taking the ratio of the number of times an event occurred to the total number of times the trials are conducted.

It can be expressed as shown below:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{times}\text{A}\text{occured}}{\text{Total}\text{number}\text{of}\text{trials}}$

Calculating the probability value

Define an event A that a boy is born to a couple.

The total number of births studied is equal to 291.

The number of boys born is equal to 239.

The probability of a boy being born is as follows:

$$\begin{gathered} P\left(A\right)=\frac{\text{Number}\text{of}\text{boys}\text{births}}{\text{Total}\text{number}\text{of}\text{births}} \\ =\frac{239}{291} \\ =0.821 \end{gathered}$$

Therefore, the probability of a boy being born is equal to 0.821.

Effectiveness of the technique

In an ideal scenario, the chance of a girl or boy child is even; 0.5.

The technique will be regarded as effective if the chance of a boy being born through the technique is significantly higher than 0.5.

As the probability of a boy being born is greater than 0.5, it can be concluded that the technique successfully increases the likelihood of birth of a male.