Question

There is a 30 percent chance of rain today and a 60 percent chance of rain tomorrow. If the two events are independent, what is the probability that it will rain today or tomorrow?

Answer 1

How many possible outcomes do we have for these two events together?

Answer 2

30/100
60/100

Answer 3

Close, but I mean how many possible ways could it rain or not rain over the next two days?

Answer 4

if the question was today and tomorrow the prob. would be .3 * .6 = .18 or 18
%

Answer 5

The question's actually ambiguous - it could refer to having rain on either today or tomorrow (but not both), or at least one of the next two days; this changes the answer.

Answer 6

P(A or B) = P(A) + P(B)

Answer 7

an 'and' related to independent events are multiplied together.
so today AND tomorrow = .3 * .6 but today OR tomorrow - are they added? - that would make 90% - seems a bit high!

Answer 8

But we are looking for P( A & B) = P(A) * P(B)

Answer 9

That's true, sorry these are unrelated.

Answer 10

If we're looking for the exclusive or (one of the two days raining), then we could just subtract the probabilities of both days raining or not raining.

Answer 11

Otherwise the probability will eventually exceed 100 ;)

Answer 12

Correct you want to find 1- P(~A AND ~B)

Answer 13

In that case, P(Day 1 Raining and Day 2 Raining) = .6 * .3 = .18

Answer 14

P(Day 1 Not Raining and Day 2 Not Raining) = .4 * .7 = .28

Answer 15

1 - P(Both Raining - P (Both Not Raining) = 1 - .18 - .28 = .54

Answer 16

hmmm - my statistics knowledge is very rusty

Answer 17

I don't think they care if it rains both days or just one of the two.

Answer 18

In the other case, then P = 1 - P(Both Not Raining) = 1 - .28 = .72

Answer 19

The probability that it will rain today or tomorrow is 1-.28 = .72

Answer 20

yes - makes sense