A number is selected at random from the set $\{1,2,3,4, \ldots, 1000\}$, then the probability of getting a number which is a perfect cube or a natural having odd number of divisors is

Question

A number is selected at random from the set $\{1,2,3,4, \ldots, 1000\}$, then the probability of getting a number which is a perfect cube or a natural having odd number of divisors is, $\frac{481}{500}$, $\frac{483}{500}$, $\frac{19}{500}$, $\frac{477}{500}$

MARKS App · Accepted Answer

The perfect cube numbers are in given set $\{1,2,3,4, \ldots \ldots, 100\}$ are $1,8,27,64,125,216$, $343,512,729,1000$ and the natural numbers having odd number of division are perfect square numbers and the perfect square numbers in given set are $1,4,9,16,25,36,49,64,81,100,121,144$, $169,196,225,256,289,324,361,400,441,484$, $529,576,625,676,729,784,841,900,961$. So required probability is $\frac{10+31-3}{1000}=\frac{38}{1000}=\frac{19}{500}$.

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