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?
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)
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.
A= Plant A flaw
B= Plant B flaw
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?
A= Stock A rises
B= Stock B rises
P(A and B)= .4
P(A and B)= P(A)P(B/A)
P(A and B)/P(A)=P(B/A)
.5 does not equal .6 so they are not independent.