Question

Clive wants to estimate the number of bees in a beehive.

Clive catches 50 bees from the beehive.
He marks each bee with a dye.
He then lets the bees go.
The next day, Clive catches 40 bees from the beehive.
8 of these bees have been marked with the dye.
Work out an estimate for the number of bees in the beehive.

Answer 1

Clive estimates the beehive population using the mark-and-recapture method. The calculation suggests there are around 250 bees in the beehive.

Clive is employing the mark-and-recapture method, a technique commonly used in ecology to estimate population sizes. The basic premise is that the proportion of marked individuals in the second sample reflects the proportion of marked individuals in the entire population. In this case, Clive marks 50 bees initially and then catches 40 bees in a subsequent sample, of which 8 are marked.

Let
`\(M\)` represent the total number of bees in the beehive. The initial proportion of marked bees is
`\((50)/(M)\)`. In the second sample, if 8 out of 40 bees are marked, the proportion becomes
`\((8)/(40) = (1)/(5)\).`

According to the mark-and-recapture formula:

`\[ \text{Initial proportion} = \text{Recaptured proportion} \]`

`\[ (50)/(M) = (1)/(5) \]`

Solving for
`\(M\)`:

`\[ M = (50)/((1)/(5)) = 250 \]`

Therefore, based on this mark-and-recapture method, Clive estimates that there are approximately 250 bees in the beehive.

Answer 2

To estimate the number of bees in the beehive, we can use the mark and recapture method. Clive caught 50 bees and marked them before releasing them. The next day, he caught 40 bees, of which 8 were marked. Using a proportion, we can estimate the total number of bees in the beehive to be 250.

Step-by-step explanation:

To estimate the number of bees in the beehive, we can use the mark and recapture method. Clive catches 50 bees and marks them with dye before releasing them. The next day, he catches 40 bees, of which 8 are marked. We can set up a proportion to estimate the total number of bees.

Let's call the total number of bees in the beehive 'x'. According to the mark and recapture method, the proportion would be:

50/x = 8/40

Cross multiplying, we get:

40 * 50 = 8 * x

Simplifying, we find:

x = (40 * 50)/8 = 250

Therefore, the estimate for the number of bees in the beehive is 250.