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A made-up shop records 400 shoppers. 160 buy bread, 100 buy milk and 40 buy both…
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 shop records shoppers. buy bread, buy milk and buy both. Find the probability that a shopper buys bread, and the probability that a shopper buys bread given that the shopper buys milk. Then find the number of shoppers who would buy both if the two were independent. Are buying bread and buying milk independent here?
Need a reminder? The key ideaShow
Two answers are independent when the share of one is the same in every group of the other, so . Then each expected count is the row total times the column total, divided by the grand total.
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. Bread. .
Step 2. Bread given milk. .
Step 3. The expected count. shoppers.
Answer: , and shoppers. The two are independent here: the share of bread buyers is the same with or without milk, and the count of both is exactly the expected count.
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