QJEEM11Ma0f50: JEE Main 2011 Mathematics - Class 12 JEEM11Ma0f50 Solution: If C and D are two events such that C ⊂ D and P ( D ) ≠ 0 ,…

Given that $$C\subset D$$ means $$C$$ is present entirely inside $$D$$. Which is shown below.

$$P\left(\frac{C}{D}\right)$$ = $$\frac{P\left(C\cap D\right)}{P\left(D\right)}$$ = $$\frac{P\left(C\right)}{P\left(D\right)}$$

As $$C\cap D$$ means common part of events C and D which is equal to C.

$$0\le P\left(D\right)\le 1$$

$$\therefore$$ $$\frac{P\left(C\right)}{P\left(D\right)}\ge P\left(C\right)$$

Note: Here we are dividing with $$P\left(D\right)$$ which is $$\le 1$$ and $$\ge 0$$, as we know on dividing with a number n in the range $$0\le n\le 1$$ we get always more than or equal to the original number.