Answer to Question #341132 in Statistics and Probability for Hilka

Question

Research has shown that 55% of new Small Medium Enterprises (SMEs) are started by graduates while 45% are started by non-graduates. It is also known that 70% of SMEs started by graduates are successful i.e. they survive beyond 3 years, while only 10% of those started by non-graduates are successful.

Required:

a) What is the probability that a new SME is successful?

Answer 1

Let $A$ denote the event "SME is started by graduate".

Let $B$ denote the event "SME is started by non-graduate".

Let $S$ denote the event "SME is successful".

$$P(S)=P(A)P(S|A)+P(B)P(S|B)$$

$$=0.55(0.7)+0.45(0.1)=0.43$$