Question #341448

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 suvived beyond 3 years, while only 10% of those started by non-graduates are successful.


a. What is the probability that a new SME is successfull

b. What is the probability that a new SME is successful and it was not started by a graduate

c. If it is know that a new SME is successful, what is the probability that it was not started by a graduatre


1
Expert's answer
2022-05-17T16:13:39-0400

Let AA denote the event "SME is started by graduate".

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

Let SS denote the event "SME is successful".

a.


P(S)=P(A)P(SA)+P(B)P(SB)P(S)=P(A)P(S|A)+P(B)P(S|B)

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

b.


P(SB)=P(B)P(SB)=0.45(0.1)=0.045P(S\cap B)=P(B)P(S|B)=0.45(0.1)=0.045

c.


P(BS)=P(B)P(SB)P(A)P(SA)+P(B)P(SB)P(B|S)=\dfrac{P(B)P(S|B)}{P(A)P(S|A)+P(B)P(S|B)}

=0.0450.430.10465=\dfrac{0.045}{0.43}\approx0.10465


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS