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Probability that it will rain during the next week is 0.54, and the
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12 Sep 2021, 21:06
12 Sep 2021, 21:06
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Question Stats:
19% (01:19) correct
80% (01:15) wrong based on 41 sessions
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Probability that it will rain during the next week is \(0.54\), and the probability that there will be a thunderstorm during the next week is \(0.68\).
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Probability that neither of these two events will occur |
\(0.32\) |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Re: Probability that it will rain during the next week is 0.54, and the
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14 Sep 2021, 11:27
14 Sep 2021, 11:27
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P(rain) = 0.54 , so P(no rain) = 0.46
P(thunder) = 0.68 , P(no thunder) = 0.32
Assuming that these are mutually exclusive, so P(no rain and no thunder) = 0.46 * 0.32 < Quantity B)
Answer is B)
P(thunder) = 0.68 , P(no thunder) = 0.32
Assuming that these are mutually exclusive, so P(no rain and no thunder) = 0.46 * 0.32 < Quantity B)
Answer is B)
Re: Probability that it will rain during the next week is 0.54, and the
[#permalink]
16 Sep 2021, 10:59
16 Sep 2021, 10:59
2
Since the sum of \(P(Rain) + P(Thunder) > 1\), we know that these events cannot be mutually exclusive. They are, however, independent events since the probability of one event does not affect the probability of the other. So we can use \(P(A) + P(B) - B + N = 1\), where \(B\) = Both events occur and \(N\) = Neither events occur.
\(P(Rain) + P(Thunder) - B + N = 1\)
Let's sub in the probabilities of both:
\(0.54 + 0.68 - B + N = 1\)
\(1.22 - B + N = 1\)
In this case, is it possible to minimize N? We can let N in this case be 0, having B be 0.22, and the equation holds within the constraints.
However, is it possible that \(P(Rain)\) is subsumed (contained) within \(P(Thunder)\)? Meaning, is it possible that \(P(Rain)\) = \(P(Both)\)? This is possible (think of the venn diagram, but putting the smaller circle within the larger circle).
Therefore, in this case, the \(P(Neither)\) = 0.32, which would be it's maximum.
So we have \(0 < P(Neither) ≤ 0.32\).
The answer is D
\(P(Rain) + P(Thunder) - B + N = 1\)
Let's sub in the probabilities of both:
\(0.54 + 0.68 - B + N = 1\)
\(1.22 - B + N = 1\)
In this case, is it possible to minimize N? We can let N in this case be 0, having B be 0.22, and the equation holds within the constraints.
However, is it possible that \(P(Rain)\) is subsumed (contained) within \(P(Thunder)\)? Meaning, is it possible that \(P(Rain)\) = \(P(Both)\)? This is possible (think of the venn diagram, but putting the smaller circle within the larger circle).
Therefore, in this case, the \(P(Neither)\) = 0.32, which would be it's maximum.
So we have \(0 < P(Neither) ≤ 0.32\).
The answer is D
