A broker at Goldman Sachs must decide among a computer stock and a beverage stoc

Question

A broker at Goldman Sachs must decide among a computer stock and a beverage stock for a client’s portfolio. There exist 5 possible computer stocks, and the probability of each being chosen is 1/5. There are four possible beverage stocks and the probability of each being chosen is 1/4.

a) Is the choice of the computer stock independent of the choice of a beverage stock? Explain why or why not.
b) Suppose that the broker decides that the computer stock is IBM and the beverage stocks is Coke-a-cola. Assuming these are independent, what is the probability the broker picks these two stocks?

Explanation / Answer

Solution:

probability of each computer from computer stock = 1 / 5 = 0.2

probability of each baverage from baverage stock = 1 / 4 = 0.25

( a )

Yes, the choise of computer stock is independent of the choice of a beverage stock,

since , the total probability of picking each aitam fom the two stocks adds to 1

and the probability of computer does not depend on the choice of a beverage stock

( b )

probability of picking computer stock IBM and baverage stock Coke-a-cola = 0.2 * 0.25 = 0.05

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