Question

Bill has a bag of 100 balls numbered from 1 to 100. What is the minimum number of balls that would have to be picked to be sure of having at least one number that is a multiple of another number already picked?

Answer 1

Step-by-step explanation:

A bag contains 100 balls numbered from 1 to 100. One ball is removed. What is the probability that the number on this ball is odd or greater than 80?

It’s a bit easier to first consider the second condition (greater than 80),

before considering the second condition (the number is odd),

in order to count all of the distinct possibilities considered “favorable”.

If one ball is removed (from the 100 balls numbered 1 to 100 inclusive),

then there are 20 possible numbers greater than 80.

Now, with 80 possible numbers remaining, the probability that the number is odd is half or 80 or 40.

Thus, we have 60 favorable numbers out of 100, so the answer is: 60/100 = 6/10.