Jesse and three of his friends are playing Poker with 32 cards, The 32 cards are of every combination of the for patterns with the numbers 1, 7-13. In this game, each player takes five cards randomly.1) Let X be the number of cards between the five Jesse got, with the number "1" on them. What is the probability function of X?2) What is the probability that Jesse will have at least three cards with the same number?3) During the evening, the four players played a number of rounds. In every round new cards were given out between the 32. Jesse decided he will stop playing after he will receive at lease three cards with the same number, in two games. What is the probability Jesse will play six games?WIll someone please help me understand how to solve this question? In part c, is it a geometric probability based on part b ?

Question

Jesse and three of his friends are playing Poker with 32 cards, The 32 cards are of every combination of the for patterns with the numbers 1, 7-13. In this game, each player takes five cards randomly.1) Let X be the number of cards between the five Jesse got, with the number &quot;1&quot; on them. What is the probability function of X?2) What is the probability that Jesse will have at least three cards with the same number?3) During the evening, the four players played a number of rounds. In every round new cards were given out between the 32. Jesse decided he will stop playing after he will receive at lease three cards with the same number, in two games. What is the probability Jesse will play six games?WIll someone please help me understand how to solve this question? In part c, is it a geometric probability based on part b ?

Macie Melton · Accepted Answer

Step 1From what I understand of your problem:1)   P  (  X  =  i  ) where i is the number of ones amongst the five cards Jesse gets in any round.Thus function of   X  ⇒  P  (  X  =  i  )  =                                                        (                                            4            i                                              )                                          ×                                                  (                                                          (              28              )                                      (              5              −              i              )                                                          )                                                                                (                                    32          5                                      )                                ,  i  =  0  ,  1  ,  2  ,  3  ,  4Step 22) P(three cards being the same in the draw) =                                                        (                                            8            1                                              )                                                  (                                                            (                                                    4              3                                                      )                                                                                                        (                                                    28              2                                                      )                                                    +                                                            (                                                    4              4                                                      )                                                                                                        (                                                    28              1                                                      )                                                    )                                                  (                                    32          5                                      )                              Step 33) Part three is an application of negative binomial distribution.Here In each round Jesse will get all cards in a round the same number  =                                                        (                                            8            1                                              )                                                  (                                                            (                                                    4              3                                                      )                                                                                                        (                                                    28              2                                                      )                                                    +                                                            (                                                    4              4                                                      )                                                                                                        (                                                    28              1                                                      )                                                    )                                                  (                                    32          5                                      )                                =  pIn each round Jesse will get all cards different than that in a round   =  1  −  p  =  q.Proabability that she will need two rounds of success in the six game                               (                                      (          4          +          2          −          1          )                4                              )                          q    4        p    2    =  (                              (                                      (          5          )                4                              )                          q    4        p    2

Jesse and three of his friends are playing Poker with 32 cards, The 32 cards are of every combination of the for patterns with the numbers 1, 7-13. In this game, each player takes five cards randomly.

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