Question

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

Answer 1

Let X = number of successes. 

p = probability of success in a single trial 

∴ p = 0.01 and q = 1 – p = 1 – 0.01 = 0.99 

∴ X ~ B(n, 0.01) 

The p.m.f. of X is given by

P(at least one success)

Hence, the number of trials required in order to have a probability greater than 0.5 of getting at least one success is \(\frac{log\, 0.5}{log\,0.99}\) or 68.