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Math Help - cards probability

  1. #1
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    cards probability

    A bag contains 8 cards numbered 1 through 8 .THe cards are mixed thoroughly and two cards are selected at random . Find the probability that both numbers are even .

    I know this should be done this way ,

    P(both numbers even)=(4C2)/(8C2)=3/14

    My question is why couldn't it be done this way :

    P(even)=1/2 so P(both number even)=(1/2)(1/2)=1/4 ??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thereddevils View Post
    A bag contains 8 cards numbered 1 through 8 .THe cards are mixed thoroughly and two cards are selected at random . Find the probability that both numbers are even .

    I know this should be done this way ,

    P(both numbers even)=(4C2)/(8C2)=3/14

    My question is why couldn't it be done this way :

    P(even)=1/2 so P(both number even)=(1/2)(1/2)=1/4 ??
    The probability that the second card is even given that the first is even is no longer 1/2.

    The required probability is that the first card is one of the four even cards from a total of eight cards times that the second is one of the three remaining even cards of a total of seven cards = 3/14

    CB
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  3. #3
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    If you split the situation into

    1. Take 2 cards at once

    2. Take 1 card, pause and then take another

    you will see the different ways you can calculate the same answer

    What you did was to take a card, replace it, then take a card again
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  4. #4
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    Quote Originally Posted by Archie Meade View Post
    If you split the situation into

    1. Take 2 cards at once

    2. Take 1 card, pause and then take another

    you will see the different ways you can calculate the same answer

    What you did was to take a card, replace it, then take a card again
    exactly , just realise that when i read captain's post . Thanks both of you !
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