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hallelujah1234
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The probability of A happening is 0.6 and the probability of 16 May 2004, 17:58
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The probability of A happening is 0.6 and the probability of B happening is 0.5. What is the maximum probability that neither A nor B happens?



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The probability of A happening is 0.6 and the probability of 16 May 2004, 19:13
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if B is a subset of A then if A does not happen B does not happen.
So P of neither A nor B occurs = 1-0.6 = 0.4

if A and B are independent events P(AB) = 0.5*0.6 = 0.30
P(neither A nor B ) = 1-0.30 = 0.70
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The probability of A happening is 0.6 and the probability of 17 May 2004, 07:38
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hallelujah1234
The probability of A happening is 0.6 and the probability of B happening is 0.5. What is the maximum probability that neither A nor B happens?
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Why does this logic not work?

probability of A NOT happening is 0.4
the probability of B NOT happening is 0.5

A&B NOT happening= .4*.5=.2
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The probability of A happening is 0.6 and the probability of 17 May 2004, 08:00
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Well, that doesn't capture the probability that BOTH A and B do not happen. You assumed that A and B do not intersect.
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The probability of A happening is 0.6 and the probability of 17 May 2004, 13:57
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hallelujah1234
The probability of A happening is 0.6 and the probability of B happening is 0.5. What is the maximum probability that neither A nor B happens?

Why does this logic not work?

probability of A NOT happening is 0.4
the probability of B NOT happening is 0.5

A&B NOT happening= .4*.5=.2
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You are correct. P(notA and notB) = P(notA).P(notB)

1-P(AB) = P[not(A and B)] = P(not A or not B) (De morgan Law)
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Paul
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The probability of A happening is 0.6 and the probability of 17 May 2004, 14:05
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Halle, if the question were reworded as follows:
What is the probability that neither A nor B happens?
Then we would not be able to find an answer without knowing whether are independent right?
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mirhaque
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The probability of A happening is 0.6 and the probability of 17 May 2004, 14:07
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hallelujah1234
mirhaque
hallelujah1234
The probability of A happening is 0.6 and the probability of B happening is 0.5. What is the maximum probability that neither A nor B happens?

Why does this logic not work?

probability of A NOT happening is 0.4
the probability of B NOT happening is 0.5

A&B NOT happening= .4*.5=.2

You are correct. P(notA and notB) = P(notA).P(notB)

1-P(AB) = P[not(A and B)] = P(not A or not B) (De morgan Law)
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Halle, can you pls tell us why the logic above not the logic below was appropriate for this question? Thank you!

P(A happens & B doesn't)+P(both happens)+P(neither happens)+P(B happens & A doesn't)=1
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The probability of A happening is 0.6 and the probability of 17 May 2004, 14:11
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mirhaque
hallelujah1234
mirhaque
[quote="hallelujah1234"]The probability of A happening is 0.6 and the probability of B happening is 0.5. What is the maximum probability that neither A nor B happens?

Why does this logic not work?

probability of A NOT happening is 0.4
the probability of B NOT happening is 0.5

A&B NOT happening= .4*.5=.2

You are correct. P(notA and notB) = P(notA).P(notB)

1-P(AB) = P[not(A and B)] = P(not A or not B) (De morgan Law)

Halle, can you pls tell us why the logic above not the logic below was appropriate for this question? Thank you!

P(A happens & B doesn't)+P(both happens)+P(neither happens)+P(B happens & A doesn't)=1[/quote]

What dew mean? The question is asking for maximum possible value of P(notA and notB), assume whatever you can.

P(A) = p
P(B) = q

P(AB)+P(A.notB)+P(notA.B)+P(notA. not B) = pq+p(1-q)+(1-p)q+(1-p)(1-q) =p+1-p = 1 (when A and B are independent)



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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