Question

In a family of 3 children, find the probability of having at least one boy.

Answer 1

Hint: We will first start by assuming that the boy is represented by B and girl by G. Then we will find the total possible outcomes of having at least one boy and then we will use the fact that probability of an event is the total favourable outcomes divided by total possible outcomes.

Complete step-by-step answer:
Now, we have been given that a family has 3 children and we have to find the probability of at least one boy.
Now, let us assume that the boy is represented by B and girl by G. So, we have the total favourable outcomes as,
I. BBB
II. BBG
III.BGG
IV.BGB
V. GGB
VI. GBB
VII. GBG
VIII.GGG
Now, we have total 8 cases as listed above for 3 children. Now, for favourable cases we have to find the cases in which there is atleast one boy. So, there must be at least one or more boy.
Now, for this scenario we have 7 cases in which there are one or more boys.
Now, we know that for the probability of an event $=\dfrac{Number\ of\ favourable\ outcomes}{Number\ of\ total\ possible\ outcomes}$
$=\dfrac{7}{8}$
Probability of having at least one boy is $\dfrac{7}{8}$.


Note: It is important to note that there are 8 outcomes for the given situation. Children might think that there are four events in total as 3 boys, 1 girl, 2 boys, 2 girls, 1 boy, 2 girls and the probability of each of these are equal but this is wrong. As for this we have to make assumptions that would lead to contradiction.