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# probability watch

1. The question is, the three events E1, E2, and E3 are defined in the same sample space. The events E1 and E3 are mutually exclusive. The events E1 and E3 are independent.

Given that P(E1)= 2/5, P(E3)= 1/3 AND P(E1 U E2)= 5/8, FIND

(a) P(E1 U E3)

(b) P(E2)

i have figured out the answer to (a) but not (b)
2. Hey there, I think there is an error in the wording of the question. If P(E1) and P(E3) are both non-zero, it's not possible for E1 and E3 to be both mutually exclusive and independent at the same time.

Independence implies: P(E1 ∩ E3) = P(E1) x P(E3)

Mutual exclusivity implies: P(E1 ∩ E3) = 0

Therefore P(E1 ∩ E3) = P(E1) x P(E3) = 0, but this is not possible because the question states that P(E1)= 2/5, P(E3)= 1/3

I think it would make more sense if the question was "The events E1 and E3 are mutually exclusive. The events E1 and E2 are independent."

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