Answer to Question #198626 in Statistics and Probability for linea

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.

Answer 1

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

Answer:

Given that,

Let A: SME is graduate

and let B: SME is successful

$P(A)=0.7, \ and\ P(\bar{A})=0.3,$

$P(B/A)=0.6,\ \ and\ P(B\bar{A})=0.1$

Now,

(a) The probability that it was not started by a graduate is

$P(\bar{A}/\bar{B})=\dfrac{ P(B/\bar{A})\cdot P(\bar{A})}{P(\bar{B}/\bar{A})\cdot P(\bar{A})+P(\bar{B}/A)\cdot P(A)}$

            $=\dfrac{(1-0.1)0.3}{(1-0.1)(0.3)+(1-0.6)(0.7)}$

              $=\dfrac{(0.7\times 0.3)}{(0.7\times 0.3)+(0.4\times 0.7)}$

             

             $=\dfrac{0.23}{0.49}=0.469$

Hence, $\boxed{P(\bar A/\bar B)=0.469}$