a bag contains several counters. some are green, some are yellow, and some are blue.

Question

a bag contains several counters. some are green, some are yellow, and some are blue. Matt counted them and found the theoretical probability of drawing a green counter is 1/8 and the theoretical probability of drawing a yellow counter is 1/4. What is the smallest number of counters that could be in the bag?

Answer 1

For these probabilities, 8 counters are needed in the bag.

1 green  (1 in 8 chance)

2 yellow (2 in 8, or 1 in 4 chance)5 blue

Answer 2

The smallest number would be the LCM of 8 an 4: 24

 

3 green, probability is 3/24, or 1/8

6 yellows, probability is 6/24, or 1/4

15 blue

Answer 3

Based on this, the theoretical probability of drawing a blue counter has to be 1 minus the other two probabilities, so that's 1 - 3/8 = 5/8.

 

You'd start by realizing that there have to be at least 8 counters in order to get probabilities that are multiples of 1/8.

 

BUT...  If there are 8 counters, then only one of them would be green.  In that case, you couldn't same "some are green" because there would not be a plural number of green.  At least that's the way I read it.

 

So you have to multiply up to the next number that would give probabilities that are multiples of 1/8, and that would be 16.