Question

There are some red counters and some green counters in a bag. At the start, 7 of the counters are red and the rest of them are green.

Cole takes a counter at random from the bag. She does not put the counter back in the bag. She then takes another counter from the bag.
The probability that the first counter is green and the second counter is red is 7/26. Work out the number of green counters in the bag at the start.

Please help!!!! :3

Answer 1

7/26=(g/(7+g))*(7/(6+g))

7/26=7g/(g^2+13g+42)

7g^2+91g+294=182g

7g^2-91g+294=0

g^2-13g+42=0

g^2-7g-6g+42=0

g(g-7)-6(g-7)=0

(g-6)(g-7)=0 since r=7, g=6...

check... total=13 counters to start with 7 red and 6 green

(6/13)(7/12)=42/156=7/26 :)