re. 130 of your new catch are untagged, meaning this is the first time that you’ve caught them. Assume drones were equally likely to be caught at all times. Before catching the second batch of drones, there were 400 tagged drones in the wild, the rest were untagged. 4) What number of drones N makes your second batch results as li
Watching all these drones buzz back and forth is giving you eyestrain. But you can’t just count every single drone - how could you ever know that you had caught them all?
You instead take the following approach: you build a taser-net that you can use to stun and catch drones (much more fun than just watching), before tagging them and re-releasing them into the wild. Working for a week, you manage to tag 400 drones, releasing them back into the wild. After waiting a week, you start catching drones again. Catching another 400 drones, you find that 270 of the drones you’ve caught are tagged, meaning you’d caught them before. 130 of your new catch are untagged, meaning this is the first time that you’ve caught them.
Assume drones were equally likely to be caught at all times. Before catching the second batch of drones, there were 400 tagged drones in the wild, the rest were untagged.
4) What number of drones N makes your second batch results as likely as possible?
5) Assuming again that the probability that N = n is proportional to the probability of catching these second batch results with n total drones in the air, find again the smallest nmax so that P(N ≤ nmax) = 0.95.
Hint:
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For 2.3 - imagine two boxes, [Box A][Box B]. How many ways can you put 270 tagged drones in Box A? How many ways can you put 130 untagged drones in Box B? How many ways can you fill both boxes? How does this connect to probability?
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2.4 asks for the value of N that makes your answer to 2.3 as large as possible. It may not be what you think.
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