**Answer: (a)\(\frac{1}{14}\)**

**Let **S = {00, 01, 02, ... , 48, 49}**. **

**n(S) = 50**

Let A be the event that the sum of the digits on the selected ticket is 8, then

A = {08, 17, 26, 35, 44} ⇒ n(A) = 5

Let B be the event that the product of the digits is zero.

Then, B = {00, 01, 02, ... , 08, 09, 10, 20, 30, 40}

⇒ n(B) = 14

∴ A ∩ B = {08} ⇒ n(A ∩ B) = 1

**∴ Required probability = \(P\big(\frac{A}{B}\big)\) **

= \(\frac{P(A\,\cap\,B)}{P(B)} =\frac{1/150}{14/50}\) = **\(\frac{1}{14}\)**