There is a 40% chance of rain on Tuesday and a 50% chance of rain on Friday. What percent chance will it rain both Tuesday and Friday?

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Mar 9, 2018


The answer is 20%.


The word "and" when applied to probabilities is best replaced with the multiplication operator. We want to calculate the probability of two events both happening, one with a probability of 40% and one with a probability of 50%. So, we need to calculate:

#40% * 50% = 20%#.

You can also test the other three options, and then add up all four, to make sure they sum to 1. This is a good way to check you've done it correctly.

Rains on Tuesday + doesn't rain on Friday: #40%*50%=20%#.
Doesn't rain on Tuesday + rains on Friday: #60%*50%=30%#.
Doesn't rain on both days: #60%*50%=30%#.

Now, if you add up all four possible combinations, they sum to 1 (as they should): #20% + 20% + 30% + 30%=1#.

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