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Math Help - Replacement and Without Replacement

  1. #1
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    Replacement and Without Replacement

    Bob and Laquisha have volunteered to serve on the Junior PromCommittee. The names of twenty volunteers, including Bob and Laquisha, are put into a bowl. If two names are randomly drawn fromthe bowl without replacement, what is the probability that Bob’s name will be drawn first and Laquisha’s name will be drawn second?

    My Work:

    Let Bob = 1

    Let Laquisha = 1

    There are 20 volunteers.

    I then decided to multiply (1/20) (1/20).

    However, the correct answer is (1/20) (1/19)

    Where did 19 comes from?

    Also, what is the difference between replacement and without replacement probability questions?

    Is there a simple formula for the two?



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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    Bob and Laquisha have volunteered to serve on the Junior PromCommittee. The names of twenty volunteers, including Bob and Laquisha, are put into a bowl. If two names are randomly drawn fromthe bowl without replacement, what is the probability that Bob’s name will be drawn first and Laquisha’s name will be drawn second?

    My Work:

    Let Bob = 1

    Let Laquisha = 1

    There are 20 volunteers.

    I then decided to multiply (1/20) (1/20).

    However, the correct answer is (1/20) (1/19) This is because Bob's name was already taken out, and not replaced. Thus, the probability of Laquisha's name being drawn now is 1/(20-1)=1/19 (since Bob is no longer one of the 20 volunteers in this list). However, if there was replacement, then you're original set up would be correct.

    Where did 19 comes from?

    Also, what is the difference between replacement and without replacement probability questions?

    Is there a simple formula for the two?


    --Chris
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  3. #3
    MHF Contributor
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    wonderful

    Quote Originally Posted by Chris L T521 View Post
    --Chris
    A great reply.

    Thanks
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