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September 4th, 2009, 08:48 AM   #1
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What proportion

Hello, this question got me a bit confused so thought I would ask:
Each day, a weather forecaster predicts whether or not it will rain. For 80% of rainy days, she correctly predicts that it will rain. For 90% of non-rainy days, she correctly predicts that it will not rain. Suppose that 10% of days are rainy and 90% are non-rainy.
a. What proportion of the forecast are correct?
b. Another forecaster always predicts that there will be no rain. What proportion of these forecasts are correct?
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September 4th, 2009, 10:36 AM   #2
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Re: What proportion

OK, what are you confused about?

Suppose there are 100 days and it rains on 10 of them. What is 80% of 10? What is 90% of 90? Add these together and you get the number of days out of 100 that the forecaster was correct; this is of course the same as her percentage.

The other forecaster is right for 0% of 10 days and 100% of 90 days. What';s the sum (and thus percentage) there?
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September 8th, 2009, 09:39 AM   #3
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Re: What proportion

Ok that explained it good, thanks!
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