What is the probability of a correct rain prediction in this weather forecast?

[nokia8650]

The weather is dreadful here. It rains on three times as many days as there are rain-free days. Luckily the daily weather forecast is fairly good. Whether the forecast is for rain or for no rain, it is correct on nine occasions out of ten.
What is the probability that the weather forecast will predict rain tomorrow?

The answer is 13/16, however I am unable to see how to arrive at this answer. Could someone please let me know of the working in order to receive this asnwer?

Thanks in advance.

 

[borgwal]

Consider N days, figure out how often it rains (on average, of course), and how often rain (x times) or no rain (N-x times) is predicted, and make that consistent with 9/10 predictions for rain and no rain being correct.

Then x/N=13/16 indeed.

 

[nokia8650]

Thanks a lot for the reply. It will rain 3 days for every one it doesn't = 3/4. How do I make this consistent with the 9/10?

Thanks

 

[gabbagabbahey]

Suppose that the probability of the weatherman predicting rain tomorrow was $P$, then the probability of him not predicting rain is ___? If he is correct 9/10 of the time, that means he is wrong 1/10 of the time...what does that mean that the total probability of it raining tomorrow is in terms of $P$?

 

[Lojzek]

A hint: the number of rainy days is the number of days with correct rain prediction plus the number of days with false no rain prediction.