Mathematics

Problem

Let the probability of success in a single independent trial be

p

and the probability of failure be

q=1-p

. a. (i) Show that the probability of obtaining at least one success in

n

independent trials is

1-q^{n}

. b. (ii) Using the result in (i), determine the smallest positive integer

n

for which the probability of at least one success exceeds

0.95

when

p=0.2

. c. (iii) Interpret the practical meaning of your answer in part (ii).