Results 1 to 3 of 3

Math Help - Stuck on a few problems

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    4

    Stuck on a few problems

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614
    Hello, kittysnyde!

    Thank you for showing your work!


    1) A university requires a student to take a math placement test
    and 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, and 40% pass the science.
    What is the probability that the student will pass both?

    \text{We have: }\:\underbrace{P(M \cup S)}_{0.8} \;=\;\underbrace{P(M)}_{0.6} + \underbrace{P(S)}_{0.4} - P(M \cap S)

    . . . . . 0.8 \;=\;0.6 + 0.4 - P(M \cap S) \quad\Rightarrow\quad P(M \cap S) \;=\;0.6 + 0.4 - 0.8

    Therefore: . P(M \cap S) \;=\;0.2 \;=\;20\%



    Your answer to #2 is correct!




    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?
    Let: A = stock A rises, B = stock B rises.

    If the events are independent, then: . P(A \cap B) \;=\;P(A)\cdot P(B)

    . . We are given: . P(A \cap B) \:=\:{\color{blue}0.40}

    . . And: . P(A)\cdot P(B) \:=\:(0.80)(0.60) \:=\:{\color{blue}0.48}

    No, they are not independent.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    4
    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. two problems I am really stuck on
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: November 13th 2011, 12:59 PM
  2. stuck on some problems
    Posted in the Algebra Forum
    Replies: 8
    Last Post: May 3rd 2010, 01:48 AM
  3. stuck on these 3 problems
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 1st 2010, 10:32 PM
  4. Stuck on these problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 29th 2008, 05:19 AM
  5. Stuck on a few problems
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 6th 2008, 08:29 PM

Search Tags


/mathhelpforum @mathhelpforum