What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?  Select the correct option: A) 2 / 15 B) 4 / 15 C) 1 / 15 D) 4 / 90 E) 5 / 60

Rationale: solution : there are a total of 90 two digit numbers . every third number will be divisible by ' 3 ' . therefore , there are 30 of those numbers that are divisible by ' 3 ' . of these 30 numbers , the numbers that are divisible by ' 5 ' are those that are multiples of ' 15 ' . i . e . numbers that are divisible by both ' 3 ' and ' 5 ' . there are 6 such numbers - - 15 , 30,45 , 60,75 and 90 . we need to find out numbers that are divisible by ' 3 ' and not by ' 5 ' , which will be : 30 â ˆ ’ 6 = 24 24 out of the 90 numbers are divisible by ' 3 ' and not by ' 5 ' . the required probability is therefore , = 24 / 90 = 4 / 15 answer is b
Answer: B