Work and Weather The probability that Mike has to work

Chapter 4, Problem 33CQ

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QUESTION:

Problem 33CQ

Work and Weather The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.

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QUESTION:

Problem 33CQ

Work and Weather The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.

ANSWER:

Solution:

Step 1 of 2:

     Let us denote the event A = the rain  

            Let the event B = mike has to work overtime

            And let the = overtime and rain

           Then,

                    P(A) = 0.5

                    P() = 0.028.

Here we need to find the probability that he will have to work overtime, given that it rains.


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