Answer to Question #194076 in Statistics and Probability for Julia

Question

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

a)If it is known that a new SME is not successful , what is the probability that it was not started by a graduate.

Answer 1

Let A be SME is graduate, B - SME is successful.

$P(A)=0.55, P(\bar A)=0.45, P(B|A)=0.7, P(B|\bar A)=0.1.$

$P(\bar A|\bar B)=\frac{(1-0.1)*0.45}{(1-0.1)*0.45+((1-0.7)*0.55}=\frac{0.405}{0.57}=0.7105.$