Question

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

Answer 1

When two dice are thrown simultaneously,all possible outcomes are :

S=$\left[\begin{array}{c}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right]$

Total number of all outcomes=$6\times 6=36$

Favourable outcomes of getting the product as 6 are: (2,3),(3,2),(1,6),(6,1)

Hence, number of favourable outcomes getting product as 6 is 4.

Probability that the product of the two numbers on the top of the die is 6

$=\frac{4}{36}$

$=\frac{1}{9}$