Question

In a family, having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is \[\dfrac{1}{4}\]
A. TRUE
B. FALSE

Answer 1

Hint: We denote Boy and Girl using initials as the variables. We take cases of 0, 1, 2 and 3 girls as our observations. Use the concept of probability to calculate probability in each case and check if the value comes equal to the given value or not.
* Probability of an event is given by dividing the number of favorable outcomes by total number of outcomes.

Complete step-by-step solution:
We are given a family with 3 children.
Then we can form four cases: 0 girl, 1 girl, 2 girls and 3 girls
Here observations are: 0 girl, 1 girl, 2 girls and 3 girls
Total number of observations is 4…………..… (1)
Since the probability of an event is given by dividing the number of favorable outcomes by total number of outcomes.
Calculate probability of each observation separately
(i) 0 Girls:
\[ \Rightarrow \]Probability (0 girls): \[ = \dfrac{1}{4}\]
(ii) 1 Girl:
\[ \Rightarrow \]Probability (1 girl): \[ = \dfrac{1}{4}\]
(i) 2 Girls:
\[ \Rightarrow \]Probability (2 girls): \[ = \dfrac{1}{4}\]
(i) 3 Girls:
\[ \Rightarrow \]Probability (3 girls): \[ = \dfrac{1}{4}\]
Since, each of the probabilities is equal to \[\dfrac{1}{4}\], the statement given in the question is TRUE.

\[\therefore \]Correct option is A.

Note: Many students make mistake of choosing FALSE option as they take all possibilities or 0, 1, 2 and 3 girls which are total 8 cases with order of events i.e. children taken in order but this is wrong procedure as we are not supposed to take in consideration the order of children. If we were to take order of children in consideration there would be 8 cases and probability of 0, 1, 2 and 3 girls would all be different. Here the observations are the cases 0 girls, 1 girl, 2 girls and 3 girls.