Question

Krishanu and Shaunak each pick an integer at random between 1 and 10, inclusive. What is the probability that the product of their numbers is more than 10

1. The probability of getting the numbers whose product is greater than 10 is 0.73.
Given that there are 10 numbers from which Krishanu and Shanunk choose numbers.
We are required to find the probability that the product of the numbers will be more than 10.
Probability is basically the likeliness of happening an event among all the events possiible.It cannot be negative.
Total outcomes possible=(1,1)(1,2)……..(1,10),(2,1),(2,2)…………….(2,10),(3,1),(3,2)…….(3,10),(4,1),(4,2)……….(4,10),(5,1),(5,2)..(5,10),(6,1),(6,2),………….(6,10),(7,1),(7,2),…….(7,10),(8,1),(8,2),………..(8,10),(9,1),(9,2),…………..(9,10),(10,1),(10,2)…………(10,10).
Combinations that gives the product greater than 10=(2,6),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8),(5,9),(5,10),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8),(6,9),(6,10),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7),(7,8),(7,9),(7,10),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(8,8),(8,9),(8,10),(9,2),(9,3),(9,4),(9,5),(9,6),(9,7),(9,8),(9,9),(9,10),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(10,10),
Number of total combinations=10*10=100
Number of combinations that gives product greater than 10=73
Probability of getting the numbers whose product is greater than 10=73/100
=0.73
Hence the probability of getting the numbers whose product is greater than 10 is 0.73.