Due to a recent energy crisis in California, rolling blackouts are necessary. Assume there is a
60% chance that the temperature will exceed 85F on any given day in July. Assume there is a 30% chance of a needed rolling blackout. There is a 20% chance both will occur. Find the probability that the temperature will exceed 85F and no rolling blackout will be needed
Probability Help?
2021-01-18 11:54 pm
回答 (2)
2021-01-19 12:47 am
The answer is 0.4
Explanation shown below:
Let the event that the temperature will exceed 85F be A, the event of needing a rolling blackout be B, and ~B the complement of B which is not needing a rolling blackout.
The prob you want to find is
Pr(A and ~B)
We know that Pr(A) = 0.6, Pr(B) = 0.3, Pr(A and B) = 0.2
Pr(~B) = 1-0.3 = 0.7
Pr(A and ~B) + Pr(A and B) = Pr(A)
=> Pr(A and ~B) + 0.2 = 0.6 => Pr(A and ~B) = 0.6-0.2 = 0.4
This can also be quickly seen using a Venn diagram.
Explanation shown below:
Let the event that the temperature will exceed 85F be A, the event of needing a rolling blackout be B, and ~B the complement of B which is not needing a rolling blackout.
The prob you want to find is
Pr(A and ~B)
We know that Pr(A) = 0.6, Pr(B) = 0.3, Pr(A and B) = 0.2
Pr(~B) = 1-0.3 = 0.7
Pr(A and ~B) + Pr(A and B) = Pr(A)
=> Pr(A and ~B) + 0.2 = 0.6 => Pr(A and ~B) = 0.6-0.2 = 0.4
This can also be quickly seen using a Venn diagram.
2021-01-19 12:01 am
I want to say .6 - .2 = .4, but I have a feeling I am missing something.
收錄日期: 2021-04-24 08:10:56
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