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Bob owns two stocks. There is an 80 percent probability that stock A will rise in price, while there is a 60 percent chance that stock B will rise in price. There is a 40 percent chance that both stocks will rise in price. Are the stock prices independent?

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Answer:

No, because P(A) x P(B) ≠ P(A∩B)

Step-by-step explanation:

In order for two events to be independent, the following relationship must be held true:

[tex]P(A)*P(B) = P(A\cap B)[/tex]

In this example, we are given that, P(A) = 0.80, P(B) = 0.60 and P(A∩B) =0.40.

[tex]P(A)*P(B) =0.80*0.60 = 0.48[/tex]

Therefore, P(A) x P(B) ≠ P(A∩B) and therefore the stock prices are not independent.

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