Question

There are 90 counters in a bag. each counter in the bag are either red or blue.

The number of red counters : The number of blue counters = 2:13

Lee is going to put some more red counters in the bag so that the probability of taking at random a red counter from the bag is 1/3. Work out the number of red counters that Lee is going to put in the bag?

Answer 1

27 red counters must be added

Explanation:

If we know that for 2 reds there are 13 blues, this adds up to 15, now, to calculate how many there are of each would be:

90/15 = 6

Which means that there are 2 * 6 = 12 red and 13 * 6 = 78 blue.

Therefore, the probability that it is currently red is:

12/90

We need to get to 1/3, to get to this value, we must add an x quantity x:

12 + x / 90 + x = 1/3

3 * 12 + 3 * x = 90 + x

3 * x - x = 90 - 36

2 * x = 54

x = 54/2

x = 27

we try:

(12 + 27) / (90 + 27) = 39/117 = 1/3

Therefore 27 red counters must be added