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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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Question Stats:
43% (02:01) correct
56% (02:04) wrong based on 241 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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Attachment:
vennDiagram.PNG [ 8.33 KiB | Viewed 12874 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?
