- #1

njh

- 19

- 4

- Homework Statement
- 52 cards, choose 4, what is the probability of getting 2 Aces and 2 Kings (in any order)

- Relevant Equations
- Denominator is the number of combinations of picking 4 cards out of 52, counting different orders of dealing the same 4 cards as different permutations but one single "combination": 52!/ (4! x (52-4)!) = 6,497,400/ 24 = 270,725 different combinations of 4 cards.

Numerator is the number of different ways to pick 2 Aces (out of 4 Aces in a deck) and 2 Kings (out of 4 Kings in a deck). Combination probability is "4 Choose 2": 4!/ (2! x (4-2)!) = 6

Multiply Numerator to account for 2 selections (2 of 4 Aces x 2 of 4 Kings) 6 x 6 = 36.

Probability of 4 cards being drawn out of 52 and those cards being 2 Aces and 2 Kings is 36/ 270,725 = 0.133%.

I have attempted the solution above and I am fairly sure that it is correct. My question is the following:

I got the correct answer by following the principles of combination probabilities, but intuitively I would have thought that drawing the 4 cards as I do above should result in the same answer. So I do not know what the 0.002% probability represents.

Thank you if anybody has a suggestion.

**What am I calculating if I multiply 4/52 x 3/51 x 4/50 x 3/49 = 144/ 6,497,400 = 0.002%.**I got the correct answer by following the principles of combination probabilities, but intuitively I would have thought that drawing the 4 cards as I do above should result in the same answer. So I do not know what the 0.002% probability represents.

Thank you if anybody has a suggestion.