JEE Main 2020 — Probability Question with Solution

Let B₁ be the event where Box-I is selected.

And B₂ be the event where Box-II is selected.

P(B₁) = P(B₂) = $$\frac{1}{2}$$

Let E be the event where selected card is non prime.

For B₁ : Prime numbers: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}

For B₂ : Prime numbers: {31, 37, 41, 43, 47}

P(E) = P(B₁) $$\times$$ $$P\left(\frac{E}{B_1}\right)$$ + P(B₂) $$\times$$ $$P\left(\frac{E}{B_2}\right)$$

= $$\frac{1}{2}\times \frac{20}{30}$$ + $$\frac{1}{2}\times \frac{15}{20}$$

Required probability :

$$P\left(\frac{B_1}{E}\right)$$ = $$\frac{P\left(B_2\right).P\left(\frac{E}{B_1}\right)}{P\left(E\right)}$$

= $$\frac{\frac{1}{2}\times \frac{20}{30}}{\frac{1}{2}\times \frac{20}{30}+\frac{1}{2}\frac{15}{20}}$$

= $$\frac{\frac{2}{3}}{\frac{2}{3}+\frac{3}{4}}$$

= $$\frac{8}{17}$$