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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Could you clarify how to find Quantity A? It seems to me that the 0.06 you calculate is just the probability of A and B both happening, and doesn't take into account the fact that Quantity A is both OR either. Should quantity A be: P(a)*(1-P(b)) + P(b)*(1-P(a)) + P(a)*P(b) = 0.14+0.18+0.06=0.38 ?
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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conway1521 wrote:
Could you clarify how to find Quantity A? It seems to me that the 0.06 you calculate is just the probability of A and B both happening, and doesn't take into account the fact that Quantity A is both OR either. Should quantity A be: P(a)*(1-P(b)) + P(b)*(1-P(a)) + P(a)*P(b) = 0.14+0.18+0.06=0.38 ?


I am quite confused like you.
According to my understanding P(either or both happening) = 1 - P (neither happening)
= 1 - (0.7* 0.8) = 1 -.56 = 0.44

Another way to figure this out is P(A)+ P(B) - P(A*B) = .2+.3-.06 = .44


Maybe I am getting the wording of the question wrong. I don't understand :(
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
conway1521 wrote:
Could you clarify how to find Quantity A? It seems to me that the 0.06 you calculate is just the probability of A and B both happening, and doesn't take into account the fact that Quantity A is both OR either. Should quantity A be: P(a)*(1-P(b)) + P(b)*(1-P(a)) + P(a)*P(b) = 0.14+0.18+0.06=0.38 ?

I consent with you as this sounds a bit logical than explanation above
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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You guys are right!

The Quantity A is indeed P(a)*(1-P(b)) + P(b)*(1-P(a)) + P(a)*P(b) = 0.14+0.24+0.06=0.44.
Fixed it!

BTW conway1521 got the formula right bikachu got both the formula and the value right! Nice team work




The whole distribution is P(a)P(b) + P(a)(1-P(b))+P(b)(1-P(a)) +(1-P(a))(1-P(b)) =1. Both occuring, A not B, B not A, both not occuring respectively.
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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The question says that probability of either or both happening.

Either means P(A or B) and both means P(A and B)

Since P(A or B) = P(A) + P(B) - P(A and B)

there is also an or between these two (either or both)
which means that we add these
so..

P(A or B) + P(A and B) = P(A) + P(B) - P(A and B) + P(A and B)

which equals P(A) + P(B) = 0.5
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
Since A is the complement of B, all you need to know is whether P(B) > .5. P(B) = .56, so answer B.
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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