mark scheme says 150 is answer but don't know how

13 Alex wants to find out how many ducks there are in a park.
One day he puts a tag on each of 30 of the ducks.
The next day he catches 40 ducks.
8 of these ducks have tags on them.
(i) Work out an estimate for the number of ducks in the park.

Reply 1

Sarvesh_t

you use the capture-recapture formula
Which is M/N =m/n
N is the population size to be estimated
M is the initial population captured and tagged, so 30 in this case
m is the number of members captured which are already tagged, 8 in this case
n is the population that are captured, 40 in this case

So you rearrange the formula to find N
N=m/n * M
So 30/8 * 40 = 150

Reply 2

texet

Original post by Sarvesh_t

I got the answer by doing:
40/8 = 5.
5 * 30 = 150.

Reply 3

MathsTutorGCSE

Dead easy.The ratio of ducks tagged to not tagged the second day is: 8:32 which simplify to 1:4. 22 ducks(tagged) are still out there so we should apply the same ratio:22: 22:88 altogether 110.Plus 40 equals 150 :smile: