Question

If I choose four cards from a standard -card deck, with replacement, what is the probability that I will end up with one card from each suit

Answers

  1. The probability that I will end up with one card from each suit is 3/32 when I choose four cards from a standard-card deck, with replacement. This can be obtained by finding probability of each draw.

    What is the required probability?

    • The probability of drawing first card is one, that is the card can be of any suite.
    • The probability of drawing second card is,      
    ⇒ 52 cards – 13 cards (1 suite) = 39 cards (remaining 3 suites)
    On the second draw, we have a (39/52)  = (3/4)  probability of drawing a different suite from the first draw
    • The probability of drawing third card is,
    ⇒ 52 cards – 26 cards (2 suite) = 26 cards (remaining 2 suites)
    On the third draw we have a (26/52) = (1/2) probability of drawing a suite different from the first two draws
    • The probability of drawing fourth card is,
    ⇒ 52 cards – 39 cards (3 suite) = 13 cards (remaining 1 suites)
    On the last draw we  have a (13/52) = (1/4) probability of drawing a different suite from the ones we  drew on the first three draws
    So  the probability = (1) (3/4) (1/2) (1/4) = 3/32
    Hence the probability that I will end up with one card from each suit is 3/32 when I choose four cards from a standard-card deck, with replacement.
       
    Learn more about probability here:
    brainly.com/question/17058636
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