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The probability that both events E and F occur is 0.42.

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The probability that both events E and F will occur is 0.42 [#permalink] New post 01 Feb 2017, 13:40
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83% (00:33) correct 16% (00:00) wrong based on 6 sessions



The probability that both events E and F will occur is 0.42

Quantity A
Quantity B
The probability that event E will occur
0.58


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.
[Reveal] Spoiler: OA

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Re: The probability that both events E and F will occur is 0.42 [#permalink] New post 06 Feb 2017, 12:57
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Explanation

A probability of 0.42 is the same as 42% or \(\frac{42}{100}\). The probability of two events occurring is the product of each individual event occurring:

\(\frac{E}{100} \times \frac{F}{100} = \frac{42}{100}\)

Can we make E greater than 58/100? Let's try to make a true math statement when E = 0.90:

\(\frac{90}{100} \times \frac{F}{100} = \frac{42}{100}\)

\(90F = 42\) and \(F = 0.467\).

Sure! If there is a 90% chance of probability that E will occur, there is a 47% chance F will occur.

Can we make E less than 58/100?

\(\frac{50}{100} \times \frac{F}{100} = \frac{42}{100}\)

\(50F = 42\) → \(F = 0.84\)

If there is a 50% chance of probability that E will occur, there is a 84% chance that F will occur.

Since we can make E both greater than and less than 0.42, it is impossible to determine the relationship on this question.

Hence option D is correct.
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Re: The probability that both events E and F will occur is 0.42 [#permalink] New post 17 Sep 2017, 04:47
Are we supposed to assume that the two events are independent if nothing is written or another hint towards answer D is that we can't say if the events are independent or not and thus we don't know how to compute the probability?
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Re: The probability that both events E and F will occur is 0.42 [#permalink] New post 17 Sep 2017, 05:42
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IlCreatore wrote:
Are we supposed to assume that the two events are independent if nothing is written or another hint towards answer D is that we can't say if the events are independent or not and thus we don't know how to compute the probability?


We consider events independent unless specified otherwise.
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The probability that both events E and F occur is 0.42. [#permalink] New post 06 Nov 2018, 14:21
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The probability that both events \(E\) and \(F\) occur is 0.42.

Quantity A
Quantity B
The probability that event \(E\) will occur
\(0.58\)


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.
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Re: The probability that both events E and F occur is 0.42. [#permalink] New post 07 Nov 2018, 04:41
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Carcass wrote:
The probability that both events \(E\) and \(F\) occur is 0.42.

Quantity A
Quantity B
The probability that event \(E\) will occur
\(0.58\)


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.



Explanation:

Given Probability of both events occurring = 0.42, but no information is provided for the individual events without which it is not possible to proceed further

Hence option D

http://en.wikipedia.org/wiki/Probability
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Re: The probability that both events E and F occur is 0.42.   [#permalink] 07 Nov 2018, 04:41
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The probability that both events E and F occur is 0.42.

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