Data Sufficiency

In the town of Z, the town lion roars on some days and not on others. If a day is chosen at random from last March, what is the probability that on that day, either the town lion roared or it rained?

(1) Last March, the lion never roared on a rainy day.

(2) Last March, the lion roared on 10 fewer days than it rained.

OA is E.

Source is MGMAT Word Translations. Can someone please solve and explain?

Thanks.

C wrote:In the town of Z, the town lion roars on some days and not on others. If a day is chosen at random from last March, what is the probability that on that day, either the town lion roared or it rained?

(1) Last March, the lion never roared on a rainy day.

(2) Last March, the lion roared on 10 fewer days than it rained.

OA is E.

Source is MGMAT Word Translations. Can someone please solve and explain?

Thanks.

Say A is the set of all days in which it rained in March
B is the set of all days in which the lion roared in March

To answer the question we need to n(A∪B)

1) A and B are independent => n(A∪B) = n (A) + n(B)

Which is not sufficient

2) n(B) <10

Which is not sufficient

Combined also we cant fine n(A∪B)

Hence E

Some more explanation

https://www.beatthegmat.com/roar-and-rain-t55146.html