CAIE FP2 2012 June — Question 6

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJune
TopicGeometric Distribution
TypeFirst success on specific trial

6 The probability that a particular type of light bulb is defective is 0.01 . A large number of these bulbs are tested, one by one. Assuming independence, find the probability that the tenth bulb tested is the first to be found defective. The first defective bulb is the \(N\) th to be tested. Write down the value of \(\mathrm { E } ( N )\). Find the least value of \(n\) such that \(\mathrm { P } ( N \leqslant n )\) is greater than 0.9 .