Question

Probability of four sons to a couple is
A. $\dfrac{1}{4}$
B. $\dfrac{1}{8}$
C. $\dfrac{1}{{16}}$
D. $\dfrac{1}{{32}}$

Answer 1

Hint: Probability is simply how likely something to happen and whenever we are unsure about the outcome of an event, we can talk about probabilities of certain outcomes. It deals with the occurrence of a random event.

Complete Answer:
There are always two chances for an event to occur. Similarly, for a couple, the possibility for their child to be either a girl or a boy is 50% for both the cases. Because the chance of having certain sex of a child is \[\dfrac{1}{2}\] and it is independent of each other. Hence, the probability of a son for the first time is \[\dfrac{1}{2}\]. Hence, the probability of four sons to be born to a couple is simply \[\dfrac{1}{2}{\text{ }} \times {\text{ }}\dfrac{1}{2}{\text{ }} \times {\text{ }}\dfrac{1}{2}{\text{ }} \times {\text{ }}\dfrac{1}{2}\] which evaluates to $\dfrac{1}{{16}}$.

So, the correct answer is option ‘C’ i.e $\dfrac{1}{{16}}$.

Additional information: Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes- how likely they are. The analysis of events governed by probability is called statistics.

Note: Probability of an event to occur is half for every case. Whenever a child is born, there is a 50% chance for the child to be either boy or a girl. An alternative method that can be used to find out the probability of four sons to be born to a couple is ${(\dfrac{1}{2})^n}$ , where \[n\] is the number of children. So, the probability becomes again $\dfrac{1}{{16}}$.