I am stuck on a few probability problems. Any help would be greatly appreciated. I put the answers I came up with, but I'm not sure if they are correct.

1) many universities require a student to take a math placement test as well as a computer science placement test. 80% of the students who take both tests pass either the math or the science test. 60% pass the math, 40% pass the science. What is the probability that the student will pass both?

A=Pass Math

B= Pass Science

P(A or B)= P(A)+P(B)-P(A and B)

P(A and B)= P(A)+P(B)-P(A or B)

P(A and B)= .6+.4-.8= .2

This indicates that nobody fails though. I guess i'm not entirely sure if he's saying that 60% of the 80% who pass on or the other pass math, or just that 60% in general pass math.

Other way would be

P(A and B)

P(A)P(B)

(.48)(.32)

2)Plant A produces 70% of the floppy disks produced by Computec and plant B produces the other 30%. 1% of those produced by plant A have a flaw, 2% produced by plant B have a flaw. What is the probability that a floppy disk produced by Computec has a flaw.

I said

A= Plant A flaw

B= Plant B flaw

P(A)=(.01)(.7)

P(B)=(.02)(.3)

P(A or B)= P(A)+P(B)= .013

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

I said

A= Stock A rises

B= Stock B rises

P(A)=.8

P(B)=.6

P(A and B)= .4

So,

P(A and B)= P(A)P(B/A)

rearranging

P(A and B)/P(A)=P(B/A)

.4/.8=.5

.5 does not equal .6 so they are not independent.