Question

Out of 50 tickets numbered 00, 01, 02, ..., 49, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7, given that the sum of the digits is 8, is ______.

Options

• `1/14`

• `3/14`

• `1/5`

• None of these

Answer 1

Out of 50 tickets numbered 00, 01, 02, ..., 49, one ticket is drawn randomly, the probability of the ticket having the product of its digits 7, given that the sum of the digits is 8, is `underlinebb(1/5)`.

Explanation:

Total number of cases = ⁵⁰C₁ = 50

Let A be the event of selecting a ticket with the sum of digits ‘8’.

Favourable cases to A are {08, 17, 26, 35, 44}.

Let B be the event of selecting a ticket with the product of its digits ‘7’.

Favourable cases to B is only {17}.

Now, `P(B/A) = (P(A ∩ B))/(P(A))`

= `(1/50)/(5/50)`

= `1/5`