A computer program selects an integer in the set \(\{k : 1 \le k \le 10,00,000\}\) at random and prints out the result. This process is repeated 1 million times. What is the probability that the value k = 1 appears in the printout atleast once ?
0.632121
Let \(n = 10^6\). In one selection, the probability that k = 1 is picked is \(\frac{1}{n}\), so the probability it is not picked is \(1 - \frac{1}{n}\).
The n selections are independent, so the probability that k = 1 never appears is \(\left(1 - \frac{1}{n}\right)^{n}\).
For large n, \(\left(1 - \frac{1}{n}\right)^{n} \approx e^{-1} \approx 0.367879\).
By the complement rule, P(at least once) \(= 1 - e^{-1} \approx 1 - 0.367879 = 0.632121\).
Hence, the answer is 0.632121.
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