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Event E and event F are independent. Is the probability that both even

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
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Event E and event F are independent. Is the probability that both even  [#permalink]

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04 May 2017, 00:21
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Difficulty:

55% (hard)

Question Stats:

44% (00:52) correct 56% (00:59) wrong based on 78 sessions

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Event E and event F are independent. Is the probability that both event E and event F will occur less than 0.3?

1) The probability that event E will occur is 0.25.
2) The probability that event F will not occur is 0.75.

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Re: Event E and event F are independent. Is the probability that both even  [#permalink]

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04 May 2017, 00:53
Since both are independent the probability that both will occur is Pa x Pb

S1 Pa = .25
This means any number less than or equal to 1 multiplied by .25 will be less than or equal to .25
Since Pb is <= 1
S 1 is sufficient

S2 ~Pb = 0.75
That means Pb = 0.25
Hence S 2 also sufficient

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Re: Event E and event F are independent. Is the probability that both even  [#permalink]

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07 May 2017, 16:58
==> In the original condition, there are 3 variables (P(E), P(F), P(E∩F)), and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), since
Event E and event F are independent, you get P(E∩F)=P(E)P(F). Also, con1)=con2), so you get P(E∩F)=P(E)P(F)=(0.25)P(F)=P(E)(1-0.75)=P(E)(0.25)<0.3, because P(E)=P(F)≤1, hence it is yes and sufficient.

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Re: Event E and event F are independent. Is the probability that both even &nbs [#permalink] 07 May 2017, 16:58
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