There is a 20 percent chance of rain today ...

Question

There is a 20 percent chance of rain today and a 80 percent chance of rain tomorrow. If the two events are independent, what is the probability that it will rain today or tomorrow?

Answer 1

Hello, thank you for taking the time to post your question!

Since the two events are independent, that means that we can use the formula

P(A U B) = P(A) + P(B) – P(A n B)

P(A n B) = P(A) x P(B) = 0.20 x 0.80 = 0.16, meaning that the full formula is

P(A U B) = 0.80 + 0.20 – 0.16

=0.84

So the probability that it will rain today or tomorrow is 0.84 or 84%

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

 

Since the two events are independent, P(A and B) = P(A)P(B).  So for example, suppose we wanted the probability of No Rain today and No Rain tomorrow.

 

P(No Rain today) = 1 - .2 = .8

P(No Rain tomorrow) = 1- .8 = .2

 

P(No Rain today AND No Rain tomorrow) = P(No Rain today)P(No Rain tomorrow) = .2 * .8 = .16

 

Using this, see if you can piece together the exact question you asked.  The logic is very similar.