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

Solution

When two dice are thrown simultaneously, the possible outcomes can be listed as:

	1	2	3	4	5	6
1	(1, 1)	(1, 2)	(1, 3)	(1, 4)	( 1, 5)	(1, 6)
2	(2, 1)	(2, 2)	(2, 3)	(2, 4)	(2, 5)	(2, 6)
3	(3, 1)	(3, 2)	(3, 3)	(3, 4)	(3, 5)	(3, 6)
4	(4, 1)	(4, 2)	(4, 3)	(4, 4)	(4, 5)	(4, 6)
5	(5, 1)	(5, 2)	(5, 3)	(5, 4)	(5, 5)	(5, 6)
6	(6, 1)	(6, 2)	(6, 3)	(6, 4)	(6, 5)	(6, 6)

∴ Total number of possible outcomes = 36
The outcomes favourable to the event the product of the two number of the top of the dice is 6 denoted by E are (1, 6), (2, 3), (3, 2) and (6, 1)
∴ Number of favourable outcomes = 4
$straight P space left parenthesis space straight E right parenthesis space equals space fraction numerator Favourable space number space of space outcomes over denominator Total space number space of space outcomes end fraction equals space 4 over 36 space equals space 1 over 9$

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Real Numbers

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

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