Respuesta :
If a and b are disjoint, then the value = 1.
If two events are mutually exclusive then the probability of them happening or occurring simultaneously is by definition zero. However, the described setting is impossible.
Let’s review the situation. At a given point in time there are four possible states of the world:
- S1 = Nothing happens.
- S2 = Only A happens.
- S3 = Only B happens.
- S4 = Both A and B happen.
We know that
Pr(S4) = 0,
since A and B are mutually exclusive. We also know that the probability of A happening is 0.2, which is in states S2 and S4, so
Pr(S2) + Pr(S4) = 0.2.
Moreover, the probability of B happening is 0.8, which is in states S3 and S4, so
Pr(S3) + Pr( S4) = 0.8.
Since PR(S4) = 0, it follows that
P(S2)= 0.2
and
Pr(S3) = 0.8.
However, that means that the probabilities of all possible states do not sum to 1 as they should for a probability distribution, since Pr(S2) + Pr(S3) is already 1. So the problem definition describes an impossible situation.
Hence the answer is if a and b are disjoint, then the value = 1.
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