Chapter 10, Problem 20A

Summary Introduction

To determine:

The probability of a couple giving birth to five girls in a row.

Introduction:

Reproductive cells which pass on genetic traits from the parent to child are produced by the process of meiosis. In order to maintain the same number of chromosomes in each generation, an organism produces gametes. The segregation of sex chromosomes and random combination of sperm and egg results in formation of males and females.

Answer to Problem 20A

There is 3.125% probability of a couple giving birth to five girls in a row.

Explanation of Solution

The chances of a child to be born as a male or a female is 50%. Gender of a child is determined by the sex chromosomes of the man. There are two types of sex chromosomes; X and Y. Individuals with two X chromosomes are female and those with an X and a Y are males. A man produces sperms that carry either X chromosome or Y chromosome. If the sperm carrying X chromosome fuses with egg of mother which carries X chromosome the resultant offspring will be a girl (XX). If the sperm carrying Y chromosome fuses with egg of mother which carries X chromosome the resultant offspring will be a boy (XY). So there are 50% chances for a child to born as a girl.

So, the probability of a couple giving birth to a girl is 1 out of 2 or $\frac{1}{2}$ .

Now the probability for the second child to also be a girl is $\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Similarly, the probability of a couple giving birth to five girls in a row

= $\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{32}=3.125\%$