The weathermen at the two TV stations in town – WET and WILD- were locked in a constant battle to come out with the most accurate forecasts.

The WET weatherman’s long-term accuracy record was 3/4; the WILD weatherman's long term accuracy record was 4/5. For the day ahead, WET predicted rain, while WILD predicted sun.

Assuming that rain and sun were as likely as one another, what were the odds of rain based on the two stations' forecasts?

If it is not going to rain, and their accuracy/inaccuracy were independent of each other, the probability of this reportage would be .25*.8=.2. If it were going to rain, the probability of this reportage would be .75*.2=.15.

Thus the probability of rain is .15/(.15+.2)= .15/.35 = 3/7.

Posted by Charlie on 2013-12-16 12:33:04