What is exhaustive events?
2007-07-25 21:18:51 · 4 answers · asked by Nora 1 in Science & Mathematics ➔ Mathematics
A and B cannot be mutually exclusive.
Note P(A∩B) = P(A) + P(B) - P(A∪B)
Now P(A) + P(B) = 1.1 and P(A∪B) ≤ 1, so P(A∩B) ≥ 0.1. So P(A∩B) ≠ 0, so A and B cannot be mutually exclusive.
A set of events is exhaustive if every possible outcome belongs to at least one of the events in the set. In other words, the union of the events is the whole sample space.
2007-07-25 21:26:23 · answer #1 · answered by Scarlet Manuka 7 · 1⤊ 0⤋
Imagine, say, A is 'red cards in a pack' and B is 'all the Kings'.
P(A)= 1/2 and P (B) = 1/13 the probability of A or B is not 1/2+1/13 because a 'red' could be a 'King'.
In another situation P(A) could be 0.75 and P(B) could be 0.35. Both could be true on their own, but there must be some overlap in the conditions for A and B because the toal is >1.
2007-07-26 05:53:10 · answer #2 · answered by Floll 1 · 0⤊ 0⤋
A and B cannot the possible outcomes of an experiment coz they add up to 1.10
so why worry if they are mutually exclusive or not?
2007-07-26 04:25:12 · answer #3 · answered by Anonymous · 0⤊ 1⤋
no
since P(AB) is not zero from addition theorem
2007-07-26 04:34:38 · answer #4 · answered by qwert 5 · 0⤊ 0⤋