Question

The probability it will rain today is 0.4 and the probability it will rain tomorrow is 0.3. The probability it will rain both days is 0.2. What is the probability it will rain today or tomorrow?

Answer 1

i need help !!!

Answer 2

I haven't done this in a while, but I think this is how it's done. Let's call rain today event A, and rain tomorrow event B:

P(A) = 0.4
P(B) = 0.3
P(A and B) = 0.2

P(A and B) = P(A) x P(B|A)
0.2 = 0.4 x P(B|A)
P(B|A) = 0.2/0.4 = 0.5

P(B|A) = the probability of event B given event A happens (the probability it rains tomorrow given it rained today)

Answer 3

We also know that the probability it rains tomorrow is 0.3. Which means:

P(B|not A) is the probability it rains tomorrow, given it did not rain today. The chance it rains today is 0.4, so the chance it doesn't rain today is 0.6

P(B) = P(B|A) + 0.6P(B|not A)
0.3 = 0.2 + 0.6P(B|not A)
P(B|not A) = 1/6



Then to find the probability it rains today or tomorrow, add up the probability on the branches where it rains today and not tomorrow, and where it doesn't rain today but does rain tomorrow.

Answer 4

thnx so much

Answer 5

No prob, hopefully that helps. I'm not 100% sure I did it correctly though, but it should help get you started.