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A made-up town has 2000 voters, and 600 of them support a new park…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up town has voters, and of them support a new park. A reporter picks voters at random, without replacement. Find the probability that all five support the park. Then find the same probability as if the picks were independent with chance each. Give six decimal places. By what percentage is the first answer smaller than the second?
Need a reminder? The key ideaShow
In a probability tree, multiply along a path and add the paths that make the event. Without replacement, the second branches use the counts that are left. From a big population the draws are almost independent.
The worked solution
Have you tried it?
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.
Step 1. Without replacement. .
Step 2. Independent. .
Step 3. The difference. .
Answer: about , , and the first is about smaller.
What it means. Five voters are a tiny part of , so treating the picks as independent changes the answer very little.
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