Probability

Question

In an area, it rains once in every three days. The local evening newspaper attempts to predict whether it rains or not in the following day. Three quarters of rainy days and three fifths of dry days are correctly predicted by the previous evening’s paper. Given that this evening’s paper predicts rain, what is the probability that it will actually rain tomorrow?

Comments

You're right srestha , it's known that it will rain once in every 3 day then there is something unknown . that is , which one day out of those 3 days...and if i talk more clearly , by this statement , questioner just told us the probability (by m/m+n kind theorem) of rain...like in 300 day it will rain any 100 days , don't know which 100 but 100 so P=100/300=1/3

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solution given is :

didn't get the circled part!

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he's applying total probability theorem.

that's what i explained in my answer.

to know the probability that you will predict rain contain two cases.

case 1 ) it will rain tomorrow (which have probability 1/3) and whatever you predicted you're right so read question carefully , you will know by those statements that this can only happen when you predicted rain.

case 2 ) it won't rain tomorrow (probability 2/3) and whatever you predicted , that went wrong case for you so read question again you will come to know that will only happen when yoy predicted rain for tomorrow.