On the trees of a coal town there are 500 pale moths and 500 dark moths…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
On the trees of a coal town there are 500 pale moths and 500 dark moths. Birds find the pale moths more easily. A pale moth survives to breed with a chance of 0.2, and a dark moth with a chance of 0.6. The survivors breed, and the population is brought back to 1000 in each generation, in the ratio of the survivors.
- What is the percentage of dark moths in the new generation?
- What is it in the generation after that?
- How many pale moths are there in the second new generation?
Need a reminder? The key ideaShow
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. dark, pale. Chances and .
Plan. Find the survivors, then the share, then repeat.
Step 1. (a) Dark survivors: . Pale survivors: . Share of dark: per cent. The new generation has dark and pale moths.
Step 2. (b) Dark survivors: . Pale survivors: . Share of dark: per cent.
Step 3. (c) The new generation has dark and pale moths.
Answer: per cent; per cent; pale moths.
Check. Each round multiplies the ratio of dark to pale by . The ratio goes , then , then , and per cent.
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