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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The probability of rain in Greg's town on Tuesday is 0.3.  Question banks Downloads My Bookmarks Reviews Important topics
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The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Question Stats: 70% (00:57) correct 29% (00:46) wrong based on 72 sessions
The probability of rain in Greg's town on Tuesday is 0.3. The probability that Greg's teacher will give him a pop quiz on Tuesday is 0.2. The event occur independently of each other.

 Quantity A Quantity B The probability that either or both events occur The probability that neither event occurs
[Reveal] Spoiler: OA Retired Moderator Joined: 07 Jun 2014
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Expert's post
Let A: be the event of Rain and B; be the event of pop Quiz.

P(A): 0.3
P(B): 0.2

P(B|A): 0 .. This probability of B occurring given that A has occurred. This is 0 because the events are independent.

Quantity A: P(a)*(1-P(b)) + P(b)*(1-P(a)) + P(a)*P(b) = 0.14+0.24+0.06=0.44

Quantity B: (1-P(A))*(1-P(B))= 0.7*0.8 =0.56

Note 1-P(A) is the probability of event A not happening.

Quantity B is greater
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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If events A and B are independent events then it is P(A)(B)
If events A and B are mutually exclusive only then it is P(A)(B)=0 Intern Joined: 23 Nov 2017
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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 ? Intern Joined: 31 Oct 2017
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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 Intern Joined: 25 Nov 2017
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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 Retired Moderator Joined: 07 Jun 2014
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Re: The probability of rain in Greg's town on Tuesday is 0.3. [#permalink]
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Expert's post
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. Re: The probability of rain in Greg's town on Tuesday is 0.3.   [#permalink] 19 Dec 2018, 09:53
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