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The probability that events A and B will both occur is 0.3
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28 Aug 2020, 10:18
28 Aug 2020, 10:18
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The probability that events A and B will both occur is 0.35.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability that event B will occur |
0.42 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Re: The probability that events A and B will both occur is 0.3
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28 Aug 2020, 10:18
28 Aug 2020, 10:18
1
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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Joined: 20 Aug 2020
Posts: 49
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Re: The probability that events A and B will both occur is 0.3
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28 Aug 2020, 11:12
28 Aug 2020, 11:12
1
Carcass wrote:
The probability that events A and B will both occur is 0.35.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability that event B will occur |
0.42 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
I think if we have a condition that events \(A\) and \(B\) are independent, it would make more sense.
Case 1: Events \(A\) and \(B\) are not independent
Then the probability that the event \(B\) occurs, \(P(B)\) can be any value between \(0\) and \(1\), inclusive.
Case 2: Events \(A\) and \(B\) are independent.
Remind that if events \(A\) and \(B\) are independent each other, then we have \(P(A∩B) = P(A)P(B)\).
We have \(P(A∩B)=P(A)P(B)=0.35\).
Then we may have \(P(A)=1, P(B)=0.35\) and \(P(A)=0.35, P(B)=1\).
We have two cases \(P(B)<0.42\) and \(P(B)>0.42\).
Therefore, D is the answer.
