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?
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:
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:
Doesn't rain on Tuesday + rains on Friday:
Doesn't rain on both days:
Now, if you add up all four possible combinations, they sum to 1 (as they should):