CONDITIONAL probability help please!?

Question

Gateway and Micron are computer stocks that frequently move together because they represent the same sector of the economy. During a 25 day period, the value of Gateway stock went up 17 days. On 10 of these 17 days, the value of Micron stock also went up.

On the 8 days when Gateway stock did not go up, Micron stock went up on 2 of these days.

If Gateway goes up, what is the conditional probability Micron goes up?

If Micron goes up, what is the conditional probability Gateway goes up?

If Micron does not go up, what is the conditional probability Gateway will go up?

Answer 1

Conditional probability just means you restrict yourself to those cases where the first event happens.

You need to first draw a Venn diagram. Put two overlapping circles labelled G (Gateway goes up) and M (Micron goes up).

The intersection is 10 (because they said that on the 10 of the 17 days both stocks went up). That leaves 7 left to put in the G circle. The next part says that on 2 days when Gateway *didn't* go up, Micron did. So put 2 in the M circle.

That's 7 + 10 + 2 = 19. That leaves 6 days when neither went up.

I've added a picture below so you can see the diagram. Now you should be able to answer the questions.

1) If Gateway goes up, what is the conditional probability Micron goes up? (10/17)
2) If Micron goes up, what is the conditional probability Gateway goes up? (10/12 or 5/6)
3) If Micron does not go up, what is the conditional probability Gateway will go up? Here you are considering the area *outside* the M circle. That is 13 days. On 7 of those days, Gateway goes up... so the probability is: (7/13)

Answer 2

Notice that micron went up on 12 days. (out of 25)

If Gateway goes up, the conditional probability Micron goes up is 10 out of 17, (as opposed to 12 out of 25). That's what makes it conditional.

There are 10 days when both Micron and Gateway go up.

If Micron goes up, the conditional probability Gateway goes up is 10/12. (10 days both of them go up, out of the 12 days Micron goes up)

If Micron does not go up (25-12 = 13 days) the conditional probability Gateway will go up is 7/13. (17 - 10 = 7 days Gateway went up but Micron did not, out of the 13 days Micron did not go up.)