Question

A couple has three children. The probability of having \[2\] sons and a daughter , if the eldest child is a son is
A.\[\dfrac{2}{3}\]
B.\[\dfrac{1}{2}\]
C.\[\dfrac{3}{4}\]
D.None of these

Answer 1

Hint: The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Complete step-by-step answer:
Random Experiment: A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty.
Sample Space: The sample pace associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space.
Event: An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E.
We know that Probability (event) \[ = \dfrac{{Number\; of \;favourable \;outcomes}}{{Total \;number\; of \;outcomes}}\]
In a family of three children, the sample space is as follows:
{(boy,boy,girl) , (boy,girl,boy) , (girl,boy,girl)}
Therefore total number of outcomes in this given situation is \[3\]
The event that the couple having \[2\] sons and a daughter , if the eldest child is a son is
{(boy,boy,girl) , (boy,girl,boy) , }
Therefore Probability (event) \[ = \dfrac{{Number\; of \;favourable \;outcomes}}{{Total \;number \;outcomes}}\]
\[ = \dfrac{2}{3}\]
Therefore option (A) is the correct answer .
So, the correct answer is “Option A”.

Note: The meaning of probability is basically the extent to which something is likely to happen. Probability of any event can be between 0 and 1 only. Probability of any event can never be greater than 1. Probability of any event can never be negative.