A number is selected at random from the set \(\{1,2,3,4, \ldots, 1000\}\), then the probability of getting a…
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
\(\frac{481}{500}\)
\(\frac{483}{500}\)
\(\frac{19}{500}\)
\(\frac{477}{500}\)
Solution
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 \(\frac{10+31-3}{1000}=\frac{38}{1000}=\frac{19}{500}\).