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# If Event A and Event B are independent, is the probability that both E

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Intern
Joined: 23 Feb 2019
Posts: 13
If Event A and Event B are independent, is the probability that both E  [#permalink]

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15 Mar 2019, 07:14
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Difficulty:

55% (hard)

Question Stats:

49% (01:06) correct 51% (01:07) wrong based on 76 sessions

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If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3?

(1) Probability that A will happen is 0.25

(2) Probability that B will NOT happen is 0.71
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: If Event A and Event B are independent, is the probability that both E  [#permalink]

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15 Mar 2019, 07:18
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1
Sagar360 wrote:
If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3?

(1) Probability that A will happen is 0.25

(2) Probability that B will NOT happen is 0.71

Notice that since events $$A$$ and $$B$$ are independent, then the probability that both occur, equals to the product of their individual probability, so $$P(A \text { and } B)=P(A)*P(B)$$. Also notice that $$0 \le P(A) \le 1$$ and $$0 \le P(B) \le1$$.

(1) Probability that $$A$$ will happen is 0.25. Now, since $$P(A)=0.25$$, then $$P(A \text { and } B)=P(A)*P(B) \le 0.25 \lt 0.3$$. Sufficient. Or consider the following: how can the probability that both Event $$A$$ and Event $$B$$ will happen be more than individual probability of each happening? So, the probability that both happen cannot be more than 0.25.

(2) Probability that B will NOT happen is 0.71. The same here: since $$P(B)=1-0.71=0.29$$, then $$P(A \text { and } B)=P(A)*P(B) \le 0.29 \lt 0.3$$. Sufficient.

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Re: If Event A and Event B are independent, is the probability that both E  [#permalink]

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16 Mar 2019, 11:04
1
D is correct

1) P(A) = .25
If P(B) = 1 (greatest value), then this would still be .25 and less than .3. So no matter what the probability of P(B), this would never be greater than .3.
SUFFICIENT

2) P(not B) = .71 or P(B) = .29. Same reasoning found in 1).
SUFFICIENT
Intern
Joined: 23 Feb 2019
Posts: 13
Re: If Event A and Event B are independent, is the probability that both E  [#permalink]

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15 Mar 2019, 07:32
Any other alternate method?

Posted from my mobile device
Intern
Joined: 15 Nov 2017
Posts: 11
Re: If Event A and Event B are independent, is the probability that both E  [#permalink]

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31 Mar 2019, 00:05
Sagar360 wrote:
If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3?

(1) Probability that A will happen is 0.25

(2) Probability that B will NOT happen is 0.71

Look for detailed and alternate solution please. will be helpful if it will be explained with an example.
Re: If Event A and Event B are independent, is the probability that both E   [#permalink] 31 Mar 2019, 00:05
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