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September 4th, 2009, 08:48 AM  #1 
Newbie Joined: Sep 2009 Posts: 15 Thanks: 0  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 nonrainy days, she correctly predicts that it will not rain. Suppose that 10% of days are rainy and 90% are nonrainy. 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? 
September 4th, 2009, 10:36 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  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? 
September 8th, 2009, 09:39 AM  #3 
Newbie Joined: Sep 2009 Posts: 15 Thanks: 0  Re: What proportion
Ok that explained it good, thanks!


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each day a weather forecast predicts whether or not it will rain,for 80% of rainy days she correctly predicts that it would rain. for 90% of non rainy days she correctly predicts that it will not rain. suppose that 10% of the days are rainy, and 90% of th,Maths.. percentage of non raining days
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