Question

There are 7 red counters in a bag.
The rest of the counters in the bag are blue,
There are more blue counters than red counters in the bag.
Two counters are to be taken at random from the bag.
The probability that there will be one counter of each colour is
7/15.
Work out the total number of counters in the bag before any counters are taken from the bag.

Answer 1

Let x be the number of counters in the bag.

Pr(red counter) is drawn first = 7/x

Pr(blue counter) is drawn first = (x-7)/x

Pr(counters will be same) = 8/15

solution:

with replacement:

P^req= 7/7+x × x/7+x= 7/15

so, the total number of counters in the bag before any counters are taken from the bag are 7/15.