SOLUTION: 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 or rain. Find the probability that he will have to

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Question 1120511: 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 or rain. Find the probability that he will have to work overtime, given that is rains.
Found 2 solutions by Alex.33, ikleyn:
Answer by Alex.33(110) About Me  (Show Source):
You can put this solution on YOUR website!
P(work overtime, given that is rains)=P(work overtime and it rains)/P(it rains)=0.028/0.5=0.056.
Wondering whyis it's like this? Check my lesson for it.
https://www.algebra.com/algebra/homework/Probability-and-statistics/change-this-name4813.lesson

Answer by ikleyn(52851) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 or rain. Find the probability that he will have to work overtime, given that is rains.
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The probability that Mike has to work overtime and it rains === the probability that he will have to work overtime, given that is rains = 0.028.


It is  THE SAME EVENT,  simply described/expressed by two different ways:


"Mike has to work overtime and it rains" === "he will have to work overtime, given that is rains".


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    In this my post the sign  "==="  means  "one thing is identically equal to the other".