A box contains 10 balls numbered 1 2 10 Suppose that two

A box contains 10 balls numbered 1, 2, . . ., 10. Suppose that two balls are selected at random with replacement from this box and the numbers on the balls are noted. Find the probability that the numbers on the two balls differ by 2 or more.

Solution

The number of cases where the difference is 1 is: (1,2),(2,3)...,(9,10)=9

Therefore the probability that the difference is 1= 9/10C2=9/45=1/5

Hence the probability that the numbers on the two balls differ by 2 or more= 1-1/5=4/5