STA-201: PRINCIPLES OF STATISTICS
CASE STUDY: TEXAS HOLD’EM
A. The probability that you are dealt pocket aces is 1/221, or 0.00452 to three significant digits. If you studied either Section 4.5 and 4.6 or Section 4.8, verify that probability.
1st Card- 4 cards that are aces out of the 52 cards in the deck. 2nd Card- You already got the 1st ace so now there’s only 3 aces out of 51 cards.
0.00452 is the probability of getting dealt “pocket aces”.
Therefore the probability is correct.
B. Using the result from part (a), obtain the probability that you are dealt “pocket kings.”
Same probability as part (a). 1st Card- 4 cards that are kings out of the 52 cards in the deck. 2nd Card- You already got the 1st king so now there’s only 3 kings out of 51 cards.
0.00452 is the probability of getting dealt “pocket kings”.
C. Using the result from part (a) and your analysis in part (b), find the probability that you are dealt a “pocket pair,” that is, two cards of the same denomination.
0.05882 is the probability of getting a pocket pair.
D. contains at least 1 card of your denomination. (Hint: Complementation Rule.)
Using the Complementation Rule you end up with this:
You already have 2 of the same card which leaves 2 still in the deck. So the probability of you getting 1 more of the same card in this situation is:
Also the probability of you getting 2 of the same card in this situation is:
Now add them together to get the actual probability because you can get 1 or more of the card in your denomination.
0.03918 is the probability of containing at least 1 card of your denomination.
E. gives you “trips,” that is, contains exactly 1 card of your denomination and 2 other unpaired cards.
1st card- 2 cards that’s your denomination out of 50. 2nd card- 48 cards that’s not your denomination out of 49. 3rd card- 44 cards that wouldn’t make a pair out of 48.
0.03592 is the probability of
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