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Re M2302 [#permalink]
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16 Sep 2014, 01:18
Official Solution: 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 \(P(B)=10.71=0.29\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.29 \lt 0.3\). Sufficient. Answer: D
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Re: M2302 [#permalink]
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03 Dec 2014, 22:13
Could you please explain this scenario.
1. Statement A provides only the probabilty of A  0.25. If the probability of B is zero, then P(A) * P(B) = 0. If the probabilty of B is nonzero, then P(A and B) cannot be greater than 0.25
2. Statement B provides the probability of B If the probability of A is zero, then P(A) * P(B) = 0.
The same scenario will hold true if the probability of either one of the event is 1.



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Re: M2302 [#permalink]
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10 Dec 2014, 21:18
coolparthi wrote: Could you please explain this scenario.
1. Statement A provides only the probabilty of A  0.25. If the probability of B is zero, then P(A) * P(B) = 0. If the probabilty of B is nonzero, then P(A and B) cannot be greater than 0.25
2. Statement B provides the probability of B If the probability of A is zero, then P(A) * P(B) = 0.
The same scenario will hold true if the probability of either one of the event is 1. I believe the question stem is asking the probability of A&B is >0.3 ? "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) provides P(A)=0.25 now P(B) can be maximum 1, in this case P(A)*P(B)=0.25*1=0.25 <0.3 min value of P(B) can be 0, in this case P(A)*P(B)=0.25*0=0 <0.3 in either case the combined probability is < 0.3, hence sufficient 2) same reasoning as 1) Ans. D)
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Re: M2302 [#permalink]
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10 Dec 2014, 23:31
JJo wrote: coolparthi wrote: Could you please explain this scenario.
1. Statement A provides only the probabilty of A  0.25. If the probability of B is zero, then P(A) * P(B) = 0. If the probabilty of B is nonzero, then P(A and B) cannot be greater than 0.25
2. Statement B provides the probability of B If the probability of A is zero, then P(A) * P(B) = 0.
The same scenario will hold true if the probability of either one of the event is 1. I believe the question stem is asking the probability of A&B is >0.3 ? "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) provides P(A)=0.25 now P(B) can be maximum 1, in this case P(A)*P(B)=0.25*1=0.25 <0.3 min value of P(B) can be 0, in this case P(A)*P(B)=0.25*0=0 <0.3 in either case the combined probability is < 0.3, hence sufficient 2) same reasoning as 1) Ans. D) Thanks. Did not realize that!!



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Re M2302 [#permalink]
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18 Mar 2015, 10:08
I think this question is good and helpful.



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Re: M2302 [#permalink]
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19 Aug 2015, 20:02
Beautiful question! When i first attempted it, i thought it was sub600 level. And i got it wrong! After seeing the solution i realized i had all the knowledge that was required to solve this question. But, this was a classic example that shows how GMAT doesn't care about what i 'know' but the way I comprehend the given info and apply what I know.
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As long as the events are independent we use general case formula P(A and B)=P(A)*P(B) where ocurrence of event A does not influence occurence of event B. We also remember that probability cannot exceed 1 for any single event or combination of the events. So the question asks whether: P(A) * P(B) > 0.3 (1) P(A) = 0.25. Let us try to apply the formula here: under what circumstances the "and" probability of the 2 independent events can be at least equal to 0.3? Given probability of A we can build the formula and see what probability we would need for the event B for the whole formula become equal to 0.3. 0.25 * P(B) = 0.3 P(B) = 0.3/0.25 = 1.2  hold on this cant be true, the probability of event cannot exceed 1. Hence the "and" probability of A and B just never can be 0.3 and/or greater than that. SUFFICIENT. (2) P(not B) = 0.71 > P(B)=0.29. Same logic  P(A) would exceed 1 which is not possible, hence SUFFICIENT to anwser the question conclusively.
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Re M2302 [#permalink]
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18 Dec 2015, 06:02
I think this is a highquality question and I agree with explanation.
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Re M2302 [#permalink]
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02 Mar 2016, 07:17
I think this the explanation isn't clear enough, please elaborate. and can you please provide a link from where i can understand probability and combinatorics



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Re: M2302 [#permalink]
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03 Mar 2016, 07:30



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Re M2302 [#permalink]
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30 Jun 2016, 06:18
The question reads that P(A and B)>0.3, but the explanation read that P(A and B) < 0.3.
What am I missing?



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Re M2302 [#permalink]
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09 Jul 2016, 04:14
I think this is a highquality question and I agree with explanation.



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Re: M2302 [#permalink]
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20 Nov 2017, 12:08
Great Question!!
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Re M2302 [#permalink]
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14 Apr 2018, 04:01
I think this is a highquality question and I agree with explanation.



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Re: M2302 [#permalink]
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04 Jul 2018, 09:11
Can we solve this with the help of venn diagram?










