Question

Suppose a poker hand contains seven cards rather than five. Compute the probabilities of the following poker hands: (a) a seven-card straight (b) four cards of one rank and three of a different rank (c) three cards of one rank and two cards of each of two different ranks (d) two cards of each of three different ranks, and a card of a fourth rank (e) three cards of one rank and four cards of each of four different ranks (f) seven cards each of different rank

Answer 1

Answer:

a) 0.00031

b)  0.0017

c)  0.31

d) 0.00018

Step-by-step explanation:

attached below is the detailed solution

Total number of 7-poker cards are 52P7 = 133784560

A) Determine the probabilities of Seven-card straight

probability of seven-card straight = 0.00031

B) Determine the probability of four cards of one rank and three of a different rank

P( four cards of one rank and three of different rank ) = 0.0017

C) Determine probability of three cards of one rank and two cards of each two different ranks

P( three cards one rank and two cards of two different ranks ) = 0.31

D) Determine probability of two cards of each of three different ranks and a card of a fourth rank

P ( two cards of each of three different ranks and a card of fourth rank ) =  0.00018