Question

Two numbers are selected at random and with replacement from the set {1, 2, 3, 4, 5, 6}.

1. What is the probability that the first one is equal to the second?
2. What is the probability that the first one is greater than the second?

Answer 1

a) 2 numbers can be selected at random WR from {1,2,3,4,5,6} in 6² ways.

Cases where 1st one is equal to the 2nd one = (1,1),(2,2), (3,3), (4,4), (5,5), (6,6)

So no. of such cases =6

hence P[that the first one is equal to the second] =

b) Cases where 1st one is greater than the 2nd one=(6,5),(6,4), (6,3), (6,2), (6,1), (5,4), (5,3), (5,2), (5,1), (4,3), (4,2), (4,1), (3,2), (3,1), (2,1).

So, no. of such cases= 15

hence P[that the 1st one is greater than the 2nd one]