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Two different dice are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.

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#### Solution

Two dice are tossed

S = [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2), 4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]

Total number of outcomes when two dice are tossed = 6 x 6= 36

Favourable events of getting the product as 6 are:

(1 x 6 = 6), (6 x 1 = 6),(2 x 3 = 6),(3 x 2 = 6)

i.e.(1,6), (6,1), (2,3), (3,2)

Favourable events of getting product as 6 = 4

P(getting product as 6) = `4/36`

= `1/9`

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