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DS Questions on probability

by knight247 » Tue Jun 21, 2011 11:27 pm
Is the probability of Arif and Alex, both being present in class, less than 0.75?
(1)Probability of Alex being present in the class is 0.7.
(2)Probability of Arif being present in the class is 0.8.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
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Source: — Data Sufficiency |

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by Ian Stewart » Wed Jun 22, 2011 12:30 am
If the probability that Alex is present is 0.7, then the probability Alex and someone else are both present can't be more than 0.7, so Statement 1 is sufficient. Statement 2 is not, since it may be that the probability is 1 that Alex is present (in which case the probability would be 0.8 both are present) or the probability might be 0 that Alex is present (in which case the probability is 0 that both are present), to look only at the two extreme scenarios. So the answer is A.
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by Geva@EconomistGMAT » Wed Jun 22, 2011 12:36 am
knight247 wrote:Is the probability of Arif and Alex, both being present in class, less than 0.75?
(1)Probability of Alex being present in the class is 0.7.
(2)Probability of Arif being present in the class is 0.8.
(A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
(D)EACH statement ALONE is sufficient to answer the question asked.
(E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Unless I'm missing something material, the answer seems to be a straightforward C.

P(alex and Arif) = p(Alex) * P (Arif), so you need both to find the probability and see whether it is less than 0.75.
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by Ian Stewart » Wed Jun 22, 2011 12:56 am
Geva@MasterGMAT wrote:
Unless I'm missing something material, the answer seems to be a straightforward C.

P(alex and Arif) = p(Alex) * P (Arif), so you need both to find the probability and see whether it is less than 0.75.
First, if P(Alex) is 0.7, then P(Alex)*P(Arif) is less than or equal to 0.7, since P(Arif) is at most 1. So we don't need both statements here.

Second, it's not at all clear that our events are independent, so it is not clear that we can even multiply our probabilities here. Maybe Arif and Alex are best friends, and when Arif cuts class, it's more likely Alex will cut class. Or perhaps they hate each other, so when Arif attends class, Alex is more likely to skip class. The way the information in the question is presented, you can only really generate inequalities here.
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by Geva@EconomistGMAT » Wed Jun 22, 2011 1:01 am
Ian Stewart wrote:
Geva@MasterGMAT wrote:
Unless I'm missing something material, the answer seems to be a straightforward C.

P(alex and Arif) = p(Alex) * P (Arif), so you need both to find the probability and see whether it is less than 0.75.
First, if P(Alex) is 0.7, then P(Alex)*P(Arif) is less than or equal to 0.7, since P(Arif) is at most 1. So we don't need both statements here.

Second, it's not at all clear that our events are independent, so it is not clear that we can even multiply our probabilities here. Maybe Arif and Alex are best friends, and when Arif cuts class, it's more likely Alex will cut class. Or perhaps they hate each other, so when Arif attends class, Alex is more likely to skip class. The way the information in the question is presented, you can only really generate inequalities here.
Good catch on the first point.

I was considering the second point as a possible trap, but decided to ignore it - I've never actually any official question test the concept of dependent probabilities - they all eliminate this facet of the material. Technically, this question allows dependent probabilities (or at least does not explicitly rule them out), but that only indicates that this is not an official question.
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by mirantdon » Tue Jun 28, 2011 1:39 am
Consider the worst case scenario for option A
ie when arif has prob =1
--> p(arif and alex) = P(alex) *p(arif)
-->0.7*1 =0.7

Hence can be answered by only A
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by amit2k9 » Tue Jun 28, 2011 11:41 pm
yupp A it is.
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