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The probability that event A occurs and event B does not occ
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07 Aug 2020, 09:32
07 Aug 2020, 09:32
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00:00
Question Stats:
42% (01:58) correct
57% (02:03) wrong based on 221 sessions
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The probability that event A occurs and event B does not occur is greater than \(\frac{1}{4}\). The probability that event B occurs and event A does not occur is greater than \(\frac{1}{4}\) . The probability that neither of the events A and B occurs is greater than \(\frac{1}{8}\).
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
Kudos for the right solution and explanation
_________________
Quantity A |
Quantity B |
The probability that both of the events A and B occur |
\( \frac{1}{4}\) |
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
Kudos for the right solution and explanation
_________________
Re: The probability that event A occurs and event B does not occ
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08 Aug 2020, 08:41
08 Aug 2020, 08:41
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5
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Attachment:
vennDiagram.PNG [ 8.33 KiB | Viewed 11088 times ]
P(A,B complement)>.25
P(A complement, B)>.25
P(A complement, B complement)> .125
We are comparing P(A, B) with 0.25
Look at the Venn diagram posted
First we notice that P(A,B complement)+ P(A complement, B)+ P(A complement, B complement)+ P(A,B)= P(S)= 1
Then we ask ourselves: when will P(A, B) be at its max?
When P(A,B complement), P(A complement, B), and P(A complement, B complement) are its lowest values.
That is when
P(A,B complement)=.25
P(A complement, B)= .25
P(A complement, B complement)= .125
Therefore
P(A,B)<1-P(A,B complement)- P(A complement, B)- P(A complement, B complement)= 1 - .25 - .25 - .125= .375
Therefore P(A,B) could be more or less than .25
Final Answer: D
General Discussion
Re: The probability that event A occurs and event B does not occ
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08 Aug 2020, 06:03
08 Aug 2020, 06:03
Explanation plz?
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Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!!
Re: The probability that event A occurs and event B does not occ
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08 Aug 2020, 10:31
08 Aug 2020, 10:31
Expert Reply
Thank you Sir.
I admire your explanation
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I admire your explanation
_________________
Re: The probability that event A occurs and event B does not occ
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10 Sep 2020, 12:03
10 Sep 2020, 12:03
can someone list an actual #, ie .4 or 3/10 for A and for B that will satisfy the original premise?
Re: The probability that event A occurs and event B does not occ
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11 Sep 2020, 05:37
11 Sep 2020, 05:37
3
1
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Carcass wrote:
The probability that event A occurs and event B does not occur is greater than \(\frac{1}{4}\). The probability that event B occurs and event A does not occur is greater than \(\frac{1}{4}\) . The probability that neither of the events A and B occurs is greater than \(\frac{1}{8}\).
Quantity A |
Quantity B |
The probability that both of the events A and B occur |
\( \frac{1}{4}\) |
We can use a Double Matrix to show all of the probabilities (for more on this watch the video below)
So, one possible case that meets all of the conditions is as follows:
In this case we get:
Quantity A: 0.35
Quantity B: 1/4
Quantity A is greater
Another possible case is as follows:
In this case we get:
Quantity A: 0.22
Quantity B: 1/4
Quantity B is greater
Answer: D
Cheers,
Brent
Double Matrix Method
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Re: The probability that event A occurs and event B does not occ
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13 Sep 2020, 05:05
13 Sep 2020, 05:05
Thank you for your great effort! Maybe I am reading the question wrong. But A occurs and B does not occur would be .35 multiplied by .13 which is not greater than 1/4. Also, do the probabilities of occurring and not occurring have to add up to 1?
Re: The probability that event A occurs and event B does not occ
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28 Aug 2022, 13:04
28 Aug 2022, 13:04
P(A, not B) > 1/4
P(not A, B) > 1/4
P(not A, not B) > 1/8
P(A, B) < 1-1/4-1/4-1/8 --> 8/8 - 2/8 - 2/8 - 1/8 --> 3/8
P(A,B)<3/8
so P(A,B) could be greater or less than 1/4=2/8
for example, 2.5/8 (greater than 1/4=2/8) or 1/8 (less than 1/4 = 2/8)
so the answer is D
P(not A, B) > 1/4
P(not A, not B) > 1/8
P(A, B) < 1-1/4-1/4-1/8 --> 8/8 - 2/8 - 2/8 - 1/8 --> 3/8
P(A,B)<3/8
so P(A,B) could be greater or less than 1/4=2/8
for example, 2.5/8 (greater than 1/4=2/8) or 1/8 (less than 1/4 = 2/8)
so the answer is D
Re: The probability that event A occurs and event B does not occ
[#permalink]
14 Sep 2023, 00:49
14 Sep 2023, 00:49
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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