EatMyDosa wrote:
kapil1 wrote:
EgmatQuantExpert wrote:
If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.
A. \(\frac{1}{30}\)
B. \(\frac{1}{15}\)
C. \(\frac{1}{9}\)
D. \(\frac{2}{15}\)
E. \(\frac{2}{9}\)
there are 10 possible sets for ordered pair of (p,q) which are {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}, {-2, -1}, {-3, -1}, {2, 1}, {3, 1}, {5, 1}
Here, the order matters, so it is permutation
Hence, total possible outcomes = 10P2 = 90
required probability = 10/90 = 1/9
C is correct.
While you arrived at the right solution, I am not sure how you arrived at the conclusion that this is a case of Permutation? Could you please elaborate.
As per my understanding, we are "selecting" two nos from the given set. And since we are interested in the product of those two nos (to be Prime), the two sets
(-2,-1) and (-1, -2) give the same result. Therefore, the order in which the two nos are chosen does not matter.
Let me know if I have missed out on something here?
I will answer this in two parts
1st partLets understand my reasoning
We know Probability = Desired number of cases / total number of cases
Now, in desired number of cases ie 10, I have considered ordered pair ie. order matter, in other words (-1,-2) is different from (-2,-1). please refer to the set above.
Similarly, to calculate total number of cases, I would have to consider permutation ie order matters (and not combination), therefore 10P2
Required prob = 1/9
2nd partIf you still have to find out the answer with combination, that also is possible, lets look into it
Now desired number of cases will 5 ie. {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}. pl see I have not taken (-1,-2) different from (-2,-1), in other words order does not matter here.
Total number of cases can be 10C2 = 45
Required prob = 5/45 = 1/9 which is same
I hope now it is clear!
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