In two dice game, the player take turns to roll both dice, they can roll as many times as they want in one turn. A player scores the sum of the two dice thrown and gradually reaches a higher score as they continue to roll. If a single number 1 is thrown on either die, the score for that whole turn is lost. Two dice are thrown simultaneously.

What is the probability of getting a product of numbers greater than 16?

Options

A. `(7)/(36)`
B. `(2)/(9)`
C. `(1)/(4)`
D. `(11)/(36)`

Answer

C

Explanation

Favourable outcomes are `{(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,6),}`
Thus number of favourable outcomes,
`n(E_(5))=7`
P(product of numbers greater than 16),
`P(E_(5))=(n(E_(5)))/(n(S))=(7)/(36)`
Thus ( c ) is correct option.