Poker is a common game in which players are dealt five cards from a deck of card
ID: 1948283 • Letter: P
Question
Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probabilities. (Use a calculator and give the answer to five decimal places.) What are the chances of being dealt a straight or a royal flush? What are the chances of being dealt two pair or better? What are the chances of being dealt a hand that will lose to four of a kind?Explanation / Answer
TOTAL NUMBER OF POSSIBLE HANDS ..
WE HAVE 52 CARDS WITH 4 SUITS AND 13 CARDS PER SUITE.
WHEN WE ARE DEALT A 5 CARDER ,DISREGARDING THE ORDER OF DEAL ,WE HAVE
C[52,5] TOTAL NUMBER OF POSSIBLE HANDS = 52!/[47!*5!]=[52*51*50*49*48*(47!)]/[5!*47!]=
=[52*51*50*49*48]/[5!]=2598960
ROYAL FLUSH
THIS COULD BE OF ANY SUIT ...
SO WE HAVE 4 POSSIBILITIES
ONCE A SUIT IS CHOSEN THEN THE OTHER POSSIBILITY IS TO ONLY GET
A,K,Q,J,10 IN THAT SUIT , OF EACH OF WHICH , THERE IS ONLY ONE CARD IN THE PACK
SO THERE IS ONLY 1*1*1*1*1=1 WAY
SO TOAL NUMBER OF POSSIBILITIES ARE 4*1=4 WAYS
SO PROBABILITY = 4/2598960 = 0.00000154..........ANSWER
PROBABILITY = 0.00000 ...ANSWER
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TWO PAIR OR BETTER
THERE ARE ...4+36+624+3744+5108+10200+54912+123552=198180
HENCE PROBABILITY = 198180/2598960=0.0762536
=0.07625...........ANSWER
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WE CAN GET 4 OF A KIND OR BETTER IN 4+36+624= 664 WAYS
SO LOSING HANDS TO 4 OF A KIND ARE =2598960-664=2598296
SO PROBABILITY = 2598296/2598960=0.9997445
=0.99974..........ANSWER