Question

2 dices are thrown together.What is the probability of
1.) Product of two number is 12
2.) Sum of two number is 7

Answer 1

i) The sample space for product of two numbers = 12 are:
(2, 6); (3 ,4): (6, 2) and (4, 3) --- 4 events
When 2 dice are thrown the total no of ordered sets $=6\times 6=36.$
Hence, the probability that the product of 2 numbers is $12=\frac{4}{36}=\frac{1}{9}$
ii) The sample space for sum of 2 numbers = 7 are
(1, 6), (2 ,5), (3, 4) (4, 3), (5, 2) and (6, 1) --- 6 evens
Hence the probability of sum of two numbers = 7 is $\frac{6}{36}=\frac{1}{6}$