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The chance of a rainy day is 1/3. If the days did not affect each other, what would be the chance…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
- The chance of a rainy day is . If the days did not affect each other, what would be the chance of two rainy days in a row?
- In the month, how many of the pairs of days in a row were both rainy? What share is that?
- What does this tell you?
Need a reminder? The key ideaShow
The month, in degrees Celsius: , , , , , . It rained on days , to and to . List all the equally likely pairs and count. For events that do not affect each other, multiply. For at least one, take the chance of none from 1. Without putting back, the second chance changes.
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. Separate days. .
Step 2. In the month. Days 8 to 10 give 2 pairs, days 17 to 20 give 3, and days 27 to 29 give 2: pairs. .
Step 3. What it tells us. is more than twice . Rain comes in spells, so the days are linked, and multiplying their chances is wrong.
Answer: ; pairs, ; the days are not separate.
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