ftce k6 math question--helppppp

Discussion in 'Multiple Subject Tests' started by amelia7, Jul 20, 2006.

  1. amelia7

    amelia7 Rookie

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    Jul 20, 2006

    Can anyone help me see how the answer to this question was derived??

    Given a drawer with 5 black crayons, 3 blue crayons, and 2 red crayons, what is the probability that you will draw two black crayons in two draws in a dark room??

    I know the answer is 2/9; but I cannot figure out how???

    Thanks for any shedding of light:)
     
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  3. TeacherGroupie

    TeacherGroupie Moderator

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    Probability is outcomes we want divided by total possible outcomes. In this case, the probability of pulling out a black crayon on the first draw would be the number of black crayons (since any one of them will do fine) divided by the total number of crayons, or

    5 black crayons
    5 + 3 + 2 total crayons

    5/10 reduces to 1/2.

    Now on the second draw, there's one fewer black crayon and one fewer crayon in all. So now the probability is

    4 black crayons
    4 + 3 + 2 crayons

    4/9 doesn't reduce.

    To calculate the probability of two events both of which have to happen, we multiply the odds together:

    1 . 4
    2 x 9

    The result, once everything that needs reducing is reduced, is 2/9.
     
  4. amelia7

    amelia7 Rookie

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    Thanks for pointing this out--I understand it. I now the separate draws and that I needed to take one away from the group for the second draw. It seems so easy now....

    One more that is probably just as easy that you may can help me with....please:)

    If a horse will probably win three races out of ten, what are the odds that he will win?

    The answer is 3:7

    * I originally thought 3:10 and was wrong.
    * I like to use proportions to solve if I can.
    I cannot get any further than this and am confused...

    3
    __ * x
    10 __
    ?


    sorry about the strange format--this may make no sense to you the way my set up appears...
     
  5. TeacherGroupie

    TeacherGroupie Moderator

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    Ah: the problem is that probability is not the same thing as odds, even though people informally use the terms interchangeably. (Which, by the way, is what makes this tricky.)

    Probability, as we've already seen, is the ratio of desired outcomes to total outcomes. The probability that the horse will win three races out of ten is - duh - 3/10.

    Odds is the ratio of desired outcomes to other outcomes. There are 10 races; if the horse wins 3, it loses (10-3) = 7. So the odds in favor of the horse winning are 3:7, or if you will 3 to 7 - that is, 3 in favor, 7 against, if you like. (Horse race odds are in fact generally quoted as odds against to odds for: so if you're at the racetrack, the odds on this horse would be quoted as 7 to 3. The higher the odds against the horse winning, the bigger the payout on your $2 win ticket if the horse does win.)
     
  6. oldsoccerlady

    oldsoccerlady Rookie

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    I'm not Teacher Groupie but I think that I can help you with this. (I'm studying for CSET Part II math and science, hence the interest in math problems).

    First pay special attention to the wording. Probability is different than odds. Odds is a betting term. When betting you wager the chances (probability) of winning verses the chances (probability) of losing. Odds are not a fraction so much as a comparison (I think, though there might be a more accurate way to describe the term odds)) So if a horse can probably win 3 times out of 10. How many times will he probably lose? Hope that helps.
     
  7. amelia7

    amelia7 Rookie

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    Yes, you have aced it again--I really dont know how I cannot recognize it--little exposure, maybe?

    Do you know of a website where I could get practice for probability and odds....

    I wish that I could have your knowledge of math for one day...saturday--perhaps, I can do this afterall....
     
  8. TeacherGroupie

    TeacherGroupie Moderator

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    Jul 21, 2006

  9. amelia7

    amelia7 Rookie

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    Thanks for the site--I have bookmarked it--I am overly exhausted from nearly 12 hours of studying today and must get some z's--however, tomorrow is the last study day and I may post some questions tomorrow--thanks!!
     
  10. TeacherGroupie

    TeacherGroupie Moderator

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    Hope you've got decently cool temperatures to sleep in by this hour.
     
  11. Pannsx4

    Pannsx4 Rookie

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    math.com is a great site for practicing.
     
  12. TeacherGroupie

    TeacherGroupie Moderator

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    Pannsx4, would you care to try your hand at these?
     
  13. Upsadaisy

    Upsadaisy Moderator

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    A simple rule to remember when figuring probability of more than one occurrence is:

    Or - means add the individual probabilities
    And - means multiply the individual probabilities

    TG - 1/6; 1/5 3/6; 3/3 2/6; 2/4
     
  14. TeacherGroupie

    TeacherGroupie Moderator

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    Yup. Bonus points to test takers who explain why 'daisy's answers make sense.
     
  15. amelia7

    amelia7 Rookie

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    Tomorrow is the test--please keep me in your thoughts. I am trying to stay positive and hope that I can put this to rest. I am taking paper and pencil version so the waiting will begin tomorrow...wish me luck and ability to remember all that is in my brain:)
     
  16. TeacherGroupie

    TeacherGroupie Moderator

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    Tomorrow, pretend that you're teaching your favorite fifth grader how to do this stuff, and answer accordingly.

    Best of luck, and don't forget to breathe.
     
  17. amelia7

    amelia7 Rookie

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    Jul 23, 2006

    Well, I am able to say that I made it through the exam--dont know if I passed or not.....but I am still alive and it took me until this afternoon to fully recooperate from the mental anguish...
    Overall, I feel okay about the outcomes. I just want to confirm that feeling in 30 days--when I get my results.

    Until then, I have put away all 300 (not kidding) of my note cards and study guides. I can only hope that I do not have to pull them out again. I begin preplanning a week from tomorrow and have lots of other things to work on before then. So, thanks again for everyone's help and I will keep you updated as time progresses.

    Lets hope the mailman will bring good results my way--I did get my score reports for the general knowledge test (sat pm after the test) to confirm that I have passed all four sections of that.........however, that endeavor did not come easy!

    Hope everyone has a wonderful week ahead!
    A
     
  18. Shontasue1

    Shontasue1 Rookie

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    Wanted to share a website I found. gohrw dot com it has tutorial videos for math, there is an actual math professor that show;s you how to do just about any problem you'd be looking at on the test. Check it out it's helping me.
     

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