# Are they pulling my leg with this maths?

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#### Thebox

• Neilep Level Member
• 3250
##### Are they pulling my leg with this maths?
« on: 03/12/2015 22:25:50 »
''In general we know;

$$P(N) = \left(\frac{4}{52}\right)^N \times \left(1-\frac{4}{52}\right)^{52-N} \times \frac{52!}{N!(52-N)!}$$

So the odds there are 4 aces in deck Y are;

$$P(4) = \left(\frac{4}{52}\right)^4 \times \left(1-\frac{4}{52}\right)^{52-4} \times \frac{52!}{4!(52-4)!} = 0.203317$$''

I have been given this maths on another forum, I do not know if this is correct. Is this correct please?

#### chiralSPO

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##### Re: Are they pulling my leg with this maths?
« Reply #1 on: 04/12/2015 00:06:16 »
These equations look good to me. I don't like the phrase "...so the odds there are 4 aces in deck Y are..." but I might be missing the context, or they might have said something they did not mean (typically the probability that a deck of cards contains 4 aces is around 100%). At just a glance, it looks like the second equation is for calculating the probability that there are 4 aces in a deck of 52 cards that was constructed by picking 52 cards from an infinite number of decks...

#### Thebox

• Neilep Level Member
• 3250
##### Re: Are they pulling my leg with this maths?
« Reply #2 on: 04/12/2015 00:22:47 »
The first equation represents 4 aces in a standard deck of 52 cards an x-axis

the second equation represents 52 random top cards (Y)  from 52 decks , showing that y only has a 20.3% chance of containing 4 aces and being even to X.

Some people have understand my poker theory and it looks like I might be correct after all.

Thank you for confirming the maths. Alan's link lead me to the maths I needed, an auto correlation link that lead me to cross correlation and  Time series analysis.

https://en.wikipedia.org/wiki/Cross-correlation

I think they used this but for 52 rather than 100 -

$$P(k) = \left(\frac{4}{52}\right)^k \times \left(1-\frac{4}{52}\right)^{100-k} \frac{100!}{k!(100-k)!}$$
« Last Edit: 04/12/2015 00:28:31 by Thebox »