Set A consists of k distinct numbers. If n numbers are selected from the set one-by-one, where n≤k, what is the probability that numbers will be selected in ascending order?
(1) Set A consists of 12 even consecutive integers.
(2) n=5.
OA is B
please give your approach
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Set A consists of k distinct numbers. If n
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sachin_yadav
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Statement 1 tells us the number of integers in the set, but not the number of numbers being selected. The number selected affects the probability of them being selected in ascending order.
For instance, if only two were selected, the probability of the lower one being selected before the higher one would be .5.
If ten were selected, without doing the math you could tell that the probability of all of them being selected in ascending order would be much lower than .5.
Insufficient.
Statement 2 tells us how many are selected, 5. Because we know how many are being selected we don't need to know how many are in set A, as at least as many are in the set as are being selected.
Further, for the purposes of determining the probability of the ones selected being selected in ascending order, only the number selected matters. The rest of the members of the set do not affect the order of selection of those being selected.
There could be five numbers in the set, 1, 2, 3, 4, and 5, and we could select them, or there could be 1000 numbers in the set and we could still select five of them. Either way we would be selecting five numbers in ascending order or not in ascending order.
You could think of the selected numbers as lowest, second lowest, middle, second highest and highest. That holds no matter how many are in the total set. So what you are calculating is the the probability of picking the lowest first and the rest in ascending order.
Therefore, without doing any math we can see that we could calculate the number of possible arrangements of 5 numbers and that we could calculate the probability of their being selected in one particular arrangement, in this case in ascending order.
Sufficient.
The correct answer is B.
For instance, if only two were selected, the probability of the lower one being selected before the higher one would be .5.
If ten were selected, without doing the math you could tell that the probability of all of them being selected in ascending order would be much lower than .5.
Insufficient.
Statement 2 tells us how many are selected, 5. Because we know how many are being selected we don't need to know how many are in set A, as at least as many are in the set as are being selected.
Further, for the purposes of determining the probability of the ones selected being selected in ascending order, only the number selected matters. The rest of the members of the set do not affect the order of selection of those being selected.
There could be five numbers in the set, 1, 2, 3, 4, and 5, and we could select them, or there could be 1000 numbers in the set and we could still select five of them. Either way we would be selecting five numbers in ascending order or not in ascending order.
You could think of the selected numbers as lowest, second lowest, middle, second highest and highest. That holds no matter how many are in the total set. So what you are calculating is the the probability of picking the lowest first and the rest in ascending order.
Therefore, without doing any math we can see that we could calculate the number of possible arrangements of 5 numbers and that we could calculate the probability of their being selected in one particular arrangement, in this case in ascending order.
Sufficient.
The correct answer is B.
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Perfect Scoring Tutor With Over a Decade of Experience
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Matt@VeritasPrep
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It's not clear whether we're selecting with or without replacement, but I'll assume it's WITH.
S1 isn't sufficient because we don't know how many numbers we're picking. (If we're only picking one, the probability is 100%, but if we're picking 12 it's ... much lower.)
S2 can be worked out algebraically. The five numbers you pick don't matter, only the order in which you pick them. But they could be picked in 5! = 120 different orders, only one of which is ascending. So your probability of getting that ascending order is 1/120.
S1 isn't sufficient because we don't know how many numbers we're picking. (If we're only picking one, the probability is 100%, but if we're picking 12 it's ... much lower.)
S2 can be worked out algebraically. The five numbers you pick don't matter, only the order in which you pick them. But they could be picked in 5! = 120 different orders, only one of which is ascending. So your probability of getting that ascending order is 1/120.
