SOLUTION: There is a 40% chance that it will be cloudy tomorrow. If it is cloudy, there is a 79% chance that it will rain. What is the probability that it will rain?

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Question 1197450: There is a 40% chance that it will be cloudy tomorrow.
If it is cloudy, there is a 79% chance that it will rain.
What is the probability that it will rain?
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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There is a 40% chance that it will be cloudy tomorrow.
If it is cloudy, there is a 79% chance that it will rain.
What is the probability that it will rain?
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            To make the problem logically complete and ready for a mathematical solution,
            I will add an additional assumption,  which is consistent with the common sense and with Physics laws.
            This addition is 

                    If it is not cloudy, then there is no rain.

            Now I am ready to solve the problem,  following the rules of probability. 


The formula for the probability is


    P(rain) = P(cloudy)*0.79 + P(not cloudy)*0 = I continue = 0.40*0.79 + (1-0.40)*0 = 0.316.    


ANSWER.  The probability is 0.316 that it will rain.

Solved.