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There is a 40% chance of rain on Monday, a 30% chance of rain on Tuesday, and a 50% chance of rain on Wednesday.  What is the probability that it will rain on exactly two days?

 May 7, 2020
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If there is a 40% chance that it will rain on Monday, then there is a 60% chance that it won't rain on Monday.

If there is a 30% chance that it will rain on Tuesday, then there is a 70% chance that it won't rain on Tuesday.

If there is a 50% chance that it will rain on Wednesday, then there is a 50% chance that it won't rain on Wednesday.

 

To rain on exactly two days:

-- rain on Monday (40%) and on Tuesday (30%) but not on Wednesday (50%)  =  0.40 x 0.30 x 0.50  =  0.06

-- rain on Monday (40%) and on Wednesday (50%) but not on Tuesday (70%)  =  0.40 x 0.50 x 0.70  =  0.14

-- rain on Tuesday (30%) and on Wednesday (50%) but not on Monday (60%)  =  0.30 x 0.50 x 0.60  =  0.09

 

Adding these individual situations:  0.06 + 0.14 + 0.09  =  0.29

 May 7, 2020

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