Vinayprajapati wrote:
Bunuel wrote:
7. 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.
We should understand following two things:
1. The probability of selecting any n numbers from the set is the same. Why should any subset of n numbers have higher or lower probability of being selected than some other subset of n numbers? Probability doesn't favor any particular subset.
2. Now, consider that the subset selected is \(\{x_1, \ x_2, \ ..., \ x_n\}\), where \(x_1<x_2<...<x_n\). We can select this subset of numbers in \(n!\) # of ways and out of these n! ways only one, namely \(\{x_1, \ x_2, \ ..., \ x_n\}\) will be in ascending order. So 1 out of n!. \(P=\frac{1}{n!}\).
Hence, according to the above the only thing we need to know to answer the question is the size of the subset (n) we are selecting from set A.
Answer: B.
One doubt dear
Lets assume k=1 2 3 4 5 6 7 8 9 10
Now if first select the number 4 then the total number i.e. k is definitely going to affect the total probability
Please clear.
Great Question Bunuel!
As for your doubt Vinay, let me try to explain it. The question does not care about the number of ways of selecting n numbers from k numbers. It is only asking for the probability of selecting numbers in increasing order.
Probability of selecting numbers in increasing order + Probability of selecting numbers in some other order = 1
Say out of the 10 numbers, you select 3 numbers. 1, 5, and 7
You can select them in increasing order = 1, 5, 7 - total 1 way
You can select them in some other order = 1, 7, 5/ 5, 1, 7/5, 7, 1/7, 5, 1/7, 1, 5 - total 5 ways
Probability of selecting numbers in increasing order = 1/6
Probability of selecting numbers in some other order = 5/6
Notice that it doesn't matter how many numbers there are in the original list. All we care about is arranging the n selected numbers. One arrangement will be in increasing order and the others will be non-increasing.
A good tricky question!
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Karishma
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