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