GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The probability that event A occurs and event B does not occ
[#permalink]
07 Aug 2020, 09:32
07 Aug 2020, 09:32
4
Expert Reply
20
Bookmarks
00:00
Question Stats:
43% (02:01) correct
56% (02:04) wrong based on 244 sessions
Hide Show timer Statistics
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
[#permalink]
08 Aug 2020, 08:41
08 Aug 2020, 08:41
2
5
Bookmarks
Attachment:
vennDiagram.PNG [ 8.33 KiB | Viewed 13103 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
[#permalink]
08 Aug 2020, 06:03
08 Aug 2020, 06:03
Explanation plz?
