Not sure of a few problems

[kittysnyde]

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.

 

[DrMike]

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 looks fine to me...

This indicates that nobody fails though

??? Why ??? It looks to me like 80% fail at least one of the tests....

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.

I think you understood the question correctly...

Other way would be

P(A and B)
P(A)P(B)

This would only apply if A and B were independent events. There's no reason to expect that they would be, and you have enough info to solve the problem without making that assumption.

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

Perfect! Well done...

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.

Yes. Or (easier) A and B are independent if and only if P(A and B)=P(A)P(B). Here, P(A and B)=.4, but P(A)P(B)=.48. These are different, so the events are not independent.

 

[kittysnyde]

Thank you!