4. -110 points My Notes Ask Your Te Gateway and Micron are computer stocks that

Question

4. -110 points My Notes Ask Your Te Gateway and Micron are computer stocks that frequently move together because they represent the same sector of the economy. For example: during a recent 25 day period, the value of Gateway stock went up 15 days. On 10 of these 15 days, the value of Micron stock also went up. However, Micron stock did go up on 2 of the 10 days when Gateway stock did not go up. Turn all these fractions into probabilities and put all the info into a tree diagram. (For example 15/25 is the probability that Gateway stock goes up, so 10/25 is the probability that it doesn't go up. And 10/15 is the conditional probability that Micron goes up if Gateway goes up, etc.) Use your tree diagram to answer the following questions. (a) What is the probability both stocks go up? (b) What is the probability neither stock goes up? (c) If Gateway goes up, what is the conditional probability Micron also goes up? (d) If Micron goes up, what is the conditional probability Gateway also goes up? (e) If Micron does not go up, what is the conditional probability Gateway will go up?

Explanation / Answer

Given probabilities:

P(Gateway up) = 15/25 = 3/5 = 0.6

P(Moron up| Gateway up) = 10/15 = 2/3

P(Moron up| Gateway didn't up) = 2/10 = 0.2

Hence,

a) P(Both goes up)

= P(Moron up| Gateway up)*P(Gateway up)

= (3/5)*(2/3)

= 2/5

= 0.40

b) P(Neither goes up)

= P(Moron didn't up| Gateway didn't up)*P(Gateway didn't up)

= 0.8*0.4

= 0.32

c) P(Moron up| Gateway up) = 10/15 = 2/3

d) P(Gateway up| Moron up) = 0.4/(0.4 + 0.2*0.4) = 5/6

e) P(Gateway up| Moron doesn't up) = (1/3 * 3/5)/(1/3 * 3/5 + 0.4*0.8) = 5/13

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