Answer:
Part A: Diagram
Psrt B:
<em><u>Joint Probability Table</u></em>
Firms Success Failure
Abercrombie 0.28 0.12
Oslon 0.36 0.24
Part C : P (O/S) =0.5625
Explanation:
The probability tree can be drawn as follows
<u><em>Part A:</em></u>
║⇒⇒P (A) = 0.4⇒⇒⇒⇒║⇒⇒⇒⇒P (S/A)= 0.7⇒⇒⇒⇒ P (A∩S)= 0.28
║ ║
║ ║⇒⇒⇒⇒ P (F/A)= 0.3⇒⇒⇒ P (A∩F)= 0.12
║
║⇒⇒⇒P (O)= 0.6⇒⇒⇒⇒║⇒⇒⇒⇒P (S/O)= 0.6⇒⇒ P (O∩S)= 0.36
║
║⇒⇒⇒P (F/O)= 0.4⇒⇒ P (O∩F)= 0.24
The marginal Probability of the two firms
P (A)= 0.4
P (O)= 0.6
Where P (A) is the probability of Abercrombie firm
P (O) is the probability of Olson firm
The conditional probabilities are given by
P (S/A)= 0.7
P (F/A)= 0.3
Where P (S/A) is the conditional probability of Success of Abercrombie firm
P (F/A) is the conditional probability of failure of Abercrombie firm
Similarly
P (S/O)= 0.6
P (F/O)= 0.4
P (S/O) is the conditional probability of Success of Oslon firm
P (F/O) is the conditional probability of failure of Oslon firm
The probability table is given by
Firms Marginal Conditional Joint
Abercrombie 0.4 0.7 0.28
0.3 0.12
Oslon 0.6 0.6 0.36
0.4 0.24
<em><u>Joint Probability Table</u></em>
Firms Success Failure
Abercrombie 0.28 0.12
Oslon 0.36 0.24
Part C :
<em><u>Using Bayes Rule: </u></em>
P (O/S) = P ( O) P( S/O)/ P ( O) P( S/O)+ P (A) P(S/ A)
= 0.6*0.6/ 0.6*0.6+0.4*0.7
=0.36/ 0.36+0.28
=0.5625