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For a certain probability experiment, P(A)=0.75 and P(B)=0.5

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Carcass
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For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   18 Sep 2019, 13:36
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For a certain probability experiment, P(A)=0.75 and P(B)=0.5. Which of the following values could be the probability that Event (A and B) will occur?

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{3}\)

D. \(\frac{2}{3}\)

E. \(\frac{3}{4}\)

OA is not provided
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 01:24
max overlap = 0.5
min overlap can be 0

Is the answer A,B,C?
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 04:22
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Carcass wrote:
For a certain probability experiment, P(A)=0.75 and P(B)=0.5. Which of the following values could be the probability that Event (A and B) will occur?

A. \(\frac{1}{6}\)

B. \(\frac{1}{5}\)

C. \(\frac{1}{3}\)

D. \(\frac{2}{3}\)

E. \(\frac{3}{4}\)

OA is not provided



If it would have been a MCQ , then it will be Option D, since there is no mention whether 2 events are independent or dependent

Here,

probability that Event (A and B) will occur = \(P(A) * P(B) = 0.75 * 0.5 = 0.375 = \frac{3}{8}\)

Hence the probability could be : Option A , Option B and Option C
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 04:24
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Wait.

This, ideally, is a single answer choice.

There is nowhere in the stem: select all the apply
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   Updated on: 19 Sep 2019, 19:42
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I read about this concept on a blog :

To find the range of overlap -

1. Max overlap = 0.5
smaller of the 2 i.e smaller of 0.75 and 0.5

2. To find min overlap :

P(AuB) = P(A) + P(B) - P(A and B) [Using max value of P(AuB) as 1 to minmise P(A and B)]
Therefore, 1 = 0.75 + 0.5 - P(A and B)
=> P(A and B) = 0.25

Hence, min overlap = 0.25

Therefore, value has to lie between 0.25 and 0.5 i.e option C (1/3 = 0.33)

Does this make sense? Why cant we assume min overlap as 0 btw?

Originally posted by fdundo on 19 Sep 2019, 04:48.
Last edited by fdundo on 19 Sep 2019, 19:42, edited 2 times in total.
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 05:03
fdundo wrote:
I read about this concept on a blog :

To find the range of overlap -

1. Max overlap = 0.5
smaller of the 2 i.e smaller of 0.75 and 0.5

2. To find min overlap : P(AuB) = P(A) + P(B) - P(A and B)

[Using max value of P(AuB) as 1 to minmise P(A and B)]

Therefore, 1 = 0.75 + 0.5 - P(A and B)
=> P(A and B) = 0.25

Therefore, value has to lie between 0.25 and 0.5 i.e option C (1/3 = 0.33)

Does this make sense? Why cant we assume min overlap as 0 btw?


yes, the range of the probability can be from 0 to 1.

Here what is the probability of P (A) + P(B) = ? . This equals to 1.25, which is greater than 1

Meaning there is an overlap , so the minimum can't be zero
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 05:08
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Great, makes sense. This was super helpful! Thanks @carcass and @pranab01
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   19 Sep 2019, 10:48
fdundo wrote:
max overlap = 0.5
min overlap can be 0

Is the answer A,B,C?


Why is the min overlap 0?
0.5 + 0.75 = 1.25 so would that imply the minimal overlap is .25?


----------------
ahhh was confirmed further down that 0 can't be the min. Is the minimal overlap .25?
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   17 Oct 2019, 12:57
Carcass can you provide the right answer?
I do think E could be the solution.
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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink] New post   17 Oct 2019, 15:45
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To be honest I strongly suggest forgetting this question because is badly worded.

The explanation provided by pranab01 above makes sense, though. Do not be foolish but the author of this post (which is me) I did not post this question.

For different reasons behind, I am in the first post but these questions are not on my radar when I post on the board.

basically it is a bad copy of the following official question https://gre.myprepclub.com/forum/qotd-19-f ... -2639.html

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Re: For a certain probability experiment, P(A)=0.75 and P(B)=0.5 [#permalink]
17 Oct 2019, 15:45
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