Question

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.
Work out an estimate for the number of ducks in the park.

Answer 1

The mark and recapture method can be used to estimate the number of ducks in the park. By tagging some ducks and then recapturing them, the population size can be estimated using an equation. In this case, the estimate is 150 ducks.

Step-by-step explanation:

One method to estimate the number of ducks in the park is the mark and recapture method. In this case, Alex puts tags on 30 ducks on the first day and catches 40 ducks on the next day, with 8 of them having tags. Using the mark and recapture equation, we can estimate the population size (N).

The equation is:

N = (M * T) / R

Where:

• N is the population size,
• M is the number of ducks tagged initially,
• T is the total number of ducks caught on the second day, and
• R is the number of ducks recaptured on the second day.

Plugging in the values, we have:

• N = (30 * 40) / 8
• N = 150

Therefore, an estimate for the number of ducks in the park is 150.

Answer 2

An estimate for the number of ducks would be 62.

There were 30 the first day.
The second day, 8 of those 30 were there as well, so we subtract that from the 40 ducks and get 32.
Add 30 and 32 to get our estimate.