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

1. Jezebel
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.