|
AP Statistics / Mr. Hansen |
Name: ____________________________ |
Poker Probabilities (5-Card Draw, not counting discards)
Instructions: Fill in the 11 missing entries in the chart, taking care to explain each number. Numbers floating around without justification will not receive credit. Note that although the answer for full house (3744) has been provided as a hint, you still need to explain how the figure of 3744 was obtained.
|
Hand |
Number of Possibilities |
Probability |
|
royal flush |
4 (one for each suit) |
4/52C5 = 0.000001539 |
|
straight flush (not incl. royal flush) |
(4 suits) (9 starting points) = 36 |
36/52C5 = 0.000013852 |
|
4 of a kind |
(13 values) (48 remaining junk cards) = 624 |
624/52C5 = 0.000240096 |
|
full house |
|
3744/52C5 = 0.001440576 |
|
flush |
(4 suits) (13C5 ways to pick 5 cards of that suit) – 36 straight flushes – 4 royal flushes = 5108; we have to be sure not to count straight and royal flushes since they were already counted above |
5108/52C5 = 0.001965402 |
|
straight |
|
|
|
3 of a kind |
|
|
|
2 pair |
|
|
|
1 pair |
|
|
|
no pair |
|
|
|
TOTAL |
52 C5 = 2,598,960 |
1.000000000 |