Question

In: Statistics and Probability

Five cards are dealt from a standard 52 card deck Determine the number of possible outcomes...

Five cards are dealt from a standard 52 card deck

  1. Determine the number of possible outcomes we could obtain
  2. What is the probability we draw
    1. Any flush (five cards of same suit)
    2. Four of a kind ( four cards of all the same rank)

Solutions

Expert Solution

a)

Total cards = 52          
number of possible outcomes of selecting 5 cards = 52C5 = 2598960          

b-a)

so, total possible ways of flush = 13C5*4 = 5148
So, P(Flush) = 5148/2598960=0.001980792

b-b)

Four of a kind-   4 cards of one denomination and one card of a second denomination.                  
there is 13 possible cases of one denomination                      
second denomination means 12 possible cases will occur                      
from 12 cases either 1 from a set (4 suit)                      
total number of ways =13C1*12C1*4C1 =   624                  
                      
P(four of a kind) = 624/2598960=   0.000240096                 

orchestra answered 2 years ago
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