A computer program select an integer in the set {k : 1≤ k ≤10,00,000} at random and prints out the result. This process is repeated 1 million times. What is…

Explanation

Probability of k = 1 in one trial = 1/1000000 = 10⁻⁶, so the probability of k ≠ 1 is 1 – 10⁻⁶. Probability that 1 is never printed in 10⁶ printouts = (1 – 10⁻⁶)^(10⁶) ≈ 1/e. Probability that 1 is printed at least once = 1 – (1 – 10⁻⁶)^(10⁶) ≈ 1 – 1/e = 0.632121.