Suppose we are playing draw poker. We are dealt 5 cards from a well-shuffled deck, which contains four spades and another card of a different suit. We decide to discard the card of a different suit and draw one card from the remaining cards to complete a flush in spades. Determine the probability of completing the flush.


closed as off-topic by TheGeekGreek, Leucippus, Sahiba Arora, Namaste, Siong Thye Goh Jul 20 '17 at 0:59

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  • $\begingroup$ As you are new to the site: people here don't tend to respond well (or at all) to questions like this that look like basic homework problems and which show no effort at all. Please edit your question to show what you have tried so far and to indicate where you are getting stuck. $\endgroup$ – lulu Jul 19 '17 at 17:48

The deck starts with 52 cards and 13 of each suit. Once the 5 cards are dealt, 47 cards remain in the deck, 9 of them being spades and 38 being the other three suits. The probability of completing the flush is the probability of pulling a spade from the remaining 47 cards. Therefore, the probability is 9/47.

Please post your work next time you ask a question so we can see what you've done and help guide you.

  • $\begingroup$ I have done it like: (13c4/52c5)*(9/47) because the probability of four spades is 13c4/52c5 and we discard the next card and then comes another spade which has a probability of 9/47. So I multiplied these two events. Is it wrong? $\endgroup$ – Walliullah Joy Jul 19 '17 at 18:26
  • $\begingroup$ The way you've worded the question it seems that you are already given 4 spades. It asks you to "determine the probability of completing a flush". It seems you're interpreting the question as "determine the probability of drawing 4 spades and 5th non-spade from a well-shuffled deck, then discarding the 5th card and completing a flush by drawing a card from the remaining deck." $\endgroup$ – B. Standage Jul 19 '17 at 18:34
  • $\begingroup$ Okie now I understand. Thank you very much! $\endgroup$ – Walliullah Joy Jul 19 '17 at 18:37
  • $\begingroup$ I'm glad I could help. $\endgroup$ – B. Standage Jul 19 '17 at 18:39

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