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Math Help - Counting Principles, card 1..50 and one number is twice the other

  1. #1
    DBA
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    Counting Principles, card 1..50 and one number is twice the other

    There are 50 cards numbered from 1 to 50.
    Two different cards are chosen at random. What is the probability that one number is twice the other number?

    The answer is 2*25 / 50*49

    I tried to split it in two cases. Case1, I get the lower card first (2,4) and case2, I get the higher number first (4,2).

    case1:

    __ __ First place has 25 choices (1-25), second place then has only 1 choice


    case2:

    __ __ First place has 25 choices (26-50), second place then has only 1 choice


    Then I would add it up: 1*25 + 1*25

    The total amount of ways to combine two cards would be 50*49 (First place has 50 choices and second place has 50-1 card which was already used)

    The probability is then 1*25 + 1*25 / 50*49

    Is this approach correct. The answer indicates that I have to multipy (2*25).

    Thanks.
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  2. #2
    MHF Contributor
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    The answer is 2*25 / 50*49
    It seems that you came up with the same answer: (1*25 + 1*25) / 50*49.

    Is this approach correct. The answer indicates that I have to multipy (2*25).
    I am not sure I understood what you said. Multiply by (2*25)?
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