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

Expert Answers
hala718 eNotes educator| Certified Educator

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.