What is the probability of a randomly chosen 2 digit number being divisible by 3 ?

Step-by-step solution

The set of all 2-digit numbers ranges from 10 to 99 . The total number of 2-digit numbers is 99 - 10 + 1 = 90 . The 2-digit numbers divisible by 3 form an arithmetic progression: 12, 15, 18, , 99 . Using the formula for the n -th term of an arithmetic progression, a_n = a + (n - 1)d , where a = 12 , d = 3 , and a_n = 99 : 99 = 12 + (n - 1)3 87 = (n - 1)3 29 = n - 1 n = 30 . The probability of choosing a 2-digit number divisible by 3 is the ratio of the number of favorable outcomes to the total number of outcomes: P