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?
+23246 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
