JEE Main 2018 — Probability Question with Solution

Let the number of children in each family be x.

Thus the total number of children in both the families are 2x

Now, it is given that 3 tickets are distributed amongst the children of these two families.

Thus, the probability that all the three tickets go to the children in family B

= $$\frac{{}^x{C}_3}{{}^{2x}{C}_3}$$ = $$\frac{1}{12}$$

$$\Rightarrow$$ $$\frac{x\left(x-1\right)\left(x-2\right)}{2x\left(2x-1\right)\left(2x-2\right)}$$ = $$\frac{1}{12}$$

$$\Rightarrow$$  $$\frac{\left(x-2\right)}{\left(2x-1\right)}$$ = $$\frac{1}{6}$$

Thus, the number of children in each family is 5.