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A royal flush in poker is when you end up with the ace, king, queen, jack, and 10 of the same suit. It's the most rare event in poker. If you are playing with a well- shuffled, legitimate deck of 52 cards, what is the probability that if you are dealt 5 cards, you will have a royal flush? Assume randomness.

Respuesta :

wolf1728

We have to determine the probability of EACH card being dealt.

1) First card can be A, K, Q, J or 10 of ANY suit.

5 cards 4 suits probability = 5*4 = 20 out of 52 p = 20/52

2) Second card must be the same suit as first card AND it must be one of the 4 remaining cards.   p = 4 / 51.  (51 because we already have 1 card)

3) Third card can only be one of the 3 remaining cards

p = 3 / 50 (There are 50 remaining cards.)

4 & 5 we can use similar reasoning for card #4 (p = 2 / 49) and

card #5 (p = 1 / 48)

Now to get the probability of being dealt a royal straight flush, we have to multiply all 5 probabilties:

20/52 * 4/51 * 3/50 * 2/49 * 1/48 = 0.00000153907716932927 which equals

1 in 649,740 which agrees with Wikipedia

https://en.wikipedia.org/wiki/Poker_probability


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