If catch and tag 100 fish and release. Later catch 85 fish. 20 have tags and 65 are not tagged. Write & solve proportion - estimate # of fish

The person catches 100 fish and tagged them, then he
releases the fish.

Let the number of all fish (tagged and
not tagged) be X.

Now we have 100 tagged fish in the
fishing area and (x-100) not tagged.

The person then
catches 85 fish out of x.

The number of tagged fish is 20
out of 85.

Now we will write and compare
probation.

==> The probability of getting a tagged
fish can be obtained as follows:

Probability (P)= Number of
tagged/ whole number of caught fish.

 ==> P = 20 /
85  = 4/17.

Now in order to find the whole number of fish,
we know that there are 100 tagged and x untagged.

Then we
apply the same probabition to get an estimate of the whole number of
fish.

==> Probability of tagged fish = number of
tagged / whole number of fish.

==>  P = 100/ x =
4/17

Now we will cross
multiply.

==> 4x =
1700

==> x =
1700/4

==> x = 425
fish.

Then, the estimate number of all fish =
425 fish.