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docker41 [41]
3 years ago
13

Suppose S and T are mutually exclusive events. Find P(S or T) if P(S) = 65% and P(T) = 7%.

Mathematics
1 answer:
iren [92.7K]3 years ago
5 0

<span>P<span>(S∪T)</span>=<span>34</span></span>

Explanation:

We use the following fundamental definition from Probability and Set Theory:

<span>P<span>(A∪B)</span>=P<span>(A)</span>+P<span>(B)</span>−P<span>(A∩B)</span></span>

And if we apply this to our problem we have:

<span>P<span>(S∪T)</span>=P<span>(S)</span>+P<span>(T)</span>−P<span>(S∩T)</span></span>
<span> =<span>13</span>+<span>512</span>−P<span>(S∩T)</span></span>
<span> =<span>34</span>−P<span>(S∩T)</span></span>

Now we are told that S and T are mutually exclusive, and so:

<span>P<span>(S∩T)</span>=0</span>

Hence,

<span>P<span>(S∪T)</span>=<span><span>34</span></span></span>

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