What proportion

Mahonroy · September 4th, 2009, 08:48 AM

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?

CRGreathouse · September 4th, 2009, 10:36 AM

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?

Mahonroy · September 8th, 2009, 09:39 AM

Ok that explained it good, thanks!

September 4th, 2009, 08:48 AM	#1
Mahonroy 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 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?
$Mahonroy is offline$

September 4th, 2009, 10:36 AM	#2
CRGreathouse 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?
$CRGreathouse is offline$

September 8th, 2009, 09:39 AM	#3
Mahonroy Newbie Joined: Sep 2009 Posts: 15 Thanks: 0	Re: What proportion Ok that explained it good, thanks!
$Mahonroy is offline$

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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