Question

Research has shown that 70% of new Small Medium Enterprises (SMEs) are started by graduates while 30% are started by non-graduates. It is also known that 60% of SMEs started by graduates are successful i.e. they survive beyond 3 years, while only 20% of those started by non-graduates are successful.

a) If it is known that a new SME has failed, what is the probability that it was started by a non-graduate? [6]

b) What is the probability that a new SME will be successful? [4

Answer 1

b) P(successful) = P(successful | graduate) * P(graduate) + P(successful | non-graduate) * P(non-graduate)

                           = 0.6 * 0.7 + 0.2 * 0.3 = 0.48

a) P(fail) = 1 - P(successful)

               = 1 - 0.48 = 0.52

P(fail | non-graduate) = 1 - P(successful | non-graduate)

                                   = 1 - 0.2 = 0.8

P(non-graduate | fail) = P(fail | non-graduate) * P(non-graduate)/P(fail)

                                        = (0.8 * 0.3)/0.52

                                        = 0.4615