JEE Main 2009 — Probability Question with Solution

Sample space = {00, 01, 02, 03, ..........49} = 50 tickets

n(S) = 50

n(Sum = 8) = { 08, 17, 26, 35, 44 } = 5

n(Product = 0) = { 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 20, 30, 40 } = 14

$$\therefore$$ Probability when product is 0 = P(Product = 0) = $$\frac{14}{50}$$

n(Sum = 8 $$\cap$$ Product = 0) = { 08 } = 1

$$\therefore$$ Probability when sum is 8 and product is 0 = P(Sum = 8 $$\cap$$ Product = 0) = $$\frac{1}{50}$$

Required probability,
$$P\left(\frac{Sum=8}{Product=0}\right)$$

= $$\frac{P\left(Sum=8\cap Product=0\right)}{P\left(Product=0\right)}$$

= $$\frac{\frac{1}{50}}{\frac{14}{50}}$$

=$$\frac{1}{14}$$

$$\therefore$$ Option (D) is correct.