Question

In Exercises 25–32, find the probability and answer the questions. XSORT Gender Selection MicroSort’s XSORT gender selection technique was designed to increase the likelihood that a baby will be a girl. At one point before clinical trials of the XSORT gender selection technique were discontinued, 945 births consisted of 879 baby girls and 66 baby boys (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a girl born to a couple using MicroSort’s XSORT method? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?

Short answer

The probability of a girl being born to a couple who have used the XSORT method is equal to 0.930.

Yes, the XSORT method is effective in increasing the probability of a girl being born.

Step-by-step solution

Given information

Through a technique known as MicroSort’s XSORT method, out of 945 births, 879 were girls, and 66 were boys.

Describe the probability of an event

The probability of an event is computed by taking the ratio of the number of outcomes in favor of the event to the total number of outcomes.

It can be expressed as shown below:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{outcomes}\text{in}\text{favour}\text{of}A}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculating the probability value

Define an event A that a girl is born to a couple using the technique.

The total number of births is equal to 945.

The number of girls born is equal to 879.

The probability of birth of a female is as follows:

$$\begin{gathered} P\left(A\right)=\frac{Numberofgirls\text{born}}{Totalnumberof\text{births}} \\ =\frac{879}{945} \\ =0.9301 \end{gathered}$$

Therefore, the probability of birth of a female is equal to 0.930.

Discuss the effectiveness of the technique

In a general setup, the chances of occurrence of boy and girl are even, with a probability equal to 0.5.

Using the technique, the chances for a girl to be born increases to 0.930, which is significantly higher than 0.5.

As the probability is extremely greater than 0.5, it can be concluded that the technique successfully increases the likelihood of birth of a female.