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Math Help - 61 cards in a deck. 22 are red, 39 are blue. Whats the % of picking a red card?

  1. #1
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    61 cards in a deck. 22 are red, 39 are blue. Whats the % of picking a red card?

    I have 61 cards in my deck. 22 are red, 39 are blue. Whats the percentage of picking up a red card?

    Another question to add to that. Lets say this was a game of cards, I have a starting hand of 7 cards, what's the percentage of getting red cards in my starting hand?

    Knowing the percentage of having X red cards in my hand, whats the percentage of getting a red card each time I draw afterwards?
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  2. #2
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    Quote Originally Posted by electricquestion View Post
    I have 61 cards in my deck. 22 are red, 39 are blue. Whats the percentage of picking up a red card?

    Another question to add to that. Lets say this was a game of cards, I have a starting hand of 7 cards, what's the percentage of getting red cards in my starting hand?

    Knowing the percentage of having X red cards in my hand, whats the percentage of getting a red card each time I draw afterwards?
    P(red) = \frac{22}{61}

    Percentage of getting red cards in hand means at least one red card in hand?

    P(R > 0) = 1 - P(R \le 0)
    P(R \le 0) = P(R = 0)
    P(R = 0) = \frac{39^7}{61*60*59*58*57*56*55}

    I am not sure I understand your last question.
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    Quote Originally Posted by colby2152 View Post
    P(red) = \frac{22}{61}

    Percentage of getting red cards in hand means at least one red card in hand?

    P(R > 0) = 1 - P(R \le 0)
    P(R \le 0) = P(R = 0)
    P(R = 0) = \frac{39^7}{61*60*59*58*57*56*55}

    I am not sure I understand your last question.
    I'm doing an experiment, and I'm trying to figure out the percentage of getting a red card in my hand the first turn, as well as the chances of getting a red card each additional draw after it.

    The last question I'm trying to figure out from the first card to the last card what my chances of drawing a red card is and whether it decreases or increases in percentages. I'm trying to map out the probability of getting a red card later in the game. In this case, having a red card is a bad thing.

    I hope this clears things up. If not I don't know what really to say but, its a card game and I'm trying to find out what odds I have in full.
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  4. #4
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    Hello, electricquestion!

    We're still unclear on the intent of your question.

    What is the object of the game?
    . . To get a red card on the first draw?
    . . To get seven red cards (when dealt seven cards)?
    . . To get a red card ... at any time?


    P(\text{Red on 1st draw} \:=\:\frac{22}{62}

    P(\text{first Red on 2nd draw}) \:=\:\frac{39}{61}\cdot\frac{22}{60}

    P(\text{first Red on 3rd draw}) \:=\:\frac{39}{61}\cdot\frac{38}{60}\cdot\frac{22}  {59}

    P(\text{first Red on 4th draw}) \:=\:\frac{39}{61}\cdot\frac{38}{60}\cdot\frac{37}  {59}\cdot\frac{22}{58}

    . . . and so on . . .

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