Conditional Probabilty question

[Mark Banford-Lawrence]

Conditional Probabilty question

[Anonymous]

There are 2 portoflios A and B. Portfolio A contains 8 stocks and 6 bonds. Portfolio B contains 8 stocks and 4 bonds. What is the the probabilty that having picked a bond it is from portoflio A

[Anonymous]

Sorry for the late response – but here it is:

Simple intuitive answer: Effectively, we are pulling a bond out of all bonds possible. Since there are a total of 10 bonds, of which 6 are in Portfolio A, therefore the probability of having picked a bond from Portfolio A is 6/10 = 60%.

Complex answer:
Let P(A) be the probability of a randomly picked security being from Portfolio A
Let P( be the probability of a randomly picked security being a Bond.

P(A) = (8+6)/(8+6+8+4) = 14/26 [prob that security is from Portfolio A]
P( = (6+4)/(8+6+8+4) = 10/26 [prob that security is a bond]
P(B|A) = 6/14 [Prob that security is a bond, given it is picked from Portfolio A]
Therefore P(A| = P(B|A)*P(A)/P( = (6/14 * 14/26)/(10/26) = 6/10 = 60%
(using Bayes’ theorem)

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