Question: If an integer is randomly selected from all positive 2-digit integers (i.e., the integers 10, 11, 12, . . . , 99), find the probability that the integer chosen has

(a) a 4 in the tens place
(b) at least one 4
(c) no 4 in either place

Ling,

There are 90 two-digit positive integers 10, 11, ..., 99. The ones that have a 4 in the tens place are 40,41,...,49. There are 10 such integers. Thus the probability that a two-digit number chosen at random will have a 4 in the tens place is

 ¹⁰/₉₀ = ¹/₉ 

How many of the 90 two-digit integers have at least one 4? How many have no 4's?

Penny