Question

Poker is a card game where you are dealt a 5 card hand from a standard deck of 52 cards. This deck has 4 suits and 13 cards per suit. The rarer your hand, the higher its worth.

(a) What is the probability of getting a “Full House”? A Full House is a hand where 3 cards share the same number or face, and the other 2 cards also share a different number or face.

(b) What is the probability of getting 5 cards from the same suit? This answer is approximately the probability of getting a “Flush”.

(c) Based off your answers above, would you bet against a Flush if you had a Full House?

Answer 1

a)

here probability of getting a “Full House =P(selecting a denomiation from 13 and then select 3 card from 4 of this denomination and then select 1 denomination from remaining 12 and select 2 card from 4 )

=¹³C₁*⁴C₃*¹²C₁*⁴C₂ /⁵²C₅ =13*4*12*6/2598960=0.001441

b)

probability of getting 5 cards from the same suit =P(select a suit from 4 and then select 5 card from13 of this suit)=⁴C₁*¹³C₅ /⁵²C₅ =4*1287/2598960=0.001981

c)

as probability of Full house is lower then flush ; therefore one should bet