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A made-up club has 20 members, and 8 of them are vegetarian…
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 club has members, and of them are vegetarian. A committee of members is chosen at random, so nobody is chosen twice. Find the probability that all three are vegetarian. Then find the answer you would get if the three were picked with replacement, as if the club were huge with the same share of vegetarians. Give four decimal places.
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. With replacement. .
Answer: about and .
Why they differ. The club is small. Each vegetarian chosen lowers the share of vegetarians left by a lot. Three members are of the club, above the rule of thumb of a tenth.
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