P(R) = prob of Roar
P(r) = prob of rain

What we need to know is P(r) U P(R)

1) we know that P(r) intersection P(R) = 0 --> They are mutually exclusive. However, what we want to know is prob of either it rained or the lion roared. So Insufficient.

2) R = r -10 ...doesnt give us enough information to calculate probabilities so Insufficient

C) together still insuff

IMO E

i agree with neoreaves.

just to clear up, we want to find:

P(roar or rain) = P(roar) + P(rain) - P(roar AND rain)

(1) makes P(roar AND rain) = 0, but we still need to find P(roar) + P(rain)

(2) gives us a relationship between roars and rain, but we still need to find at least one of those unknowns to find the other.

==> E

I am confused why the correct answer is not C. If we know there are 30 days in March, from A the lion never roared on a rainy day, and B the lion roared on 10 fewer days than it rained, then wouldnt the only possibility be roared 10/30 and rained 20/30?

I am confused why the correct answer is not C. If we know there are 30 days in March, from A the lion never roared on a rainy day, and B the lion roared on 10 fewer days than it rained, then wouldnt the only possibility be roared 10/30 and rained 20/30?

There are 31 days in March, but the split could be 10-20, 9-19, 8-18, etc. The '10 fewer' in statement (2) is the tricky part... it's not saying that then lion roared on 10 days, it's saying that the difference between the number of days the lion roared and the number of days it rained is 10. Since the statements don't give us any information about how many days neither of the two happened, we can't determine the probability.