# Thread: Probability Problem >> Very easy

1. ## Probability Problem >> Very easy

I keep getting an error every time I try to do calculations with large numbers. I was wondering if there was another way to do these problems or a way to simplify them. As you can see, with smaller numbers I can put them into my calculator and get an answer:

If you flip a coin 50 times, what is the chance you will get 25 heads?

$\displaystyle \frac{n!}{h!(h-n)!}(2^n)$

$\displaystyle \frac{50!}{25!(50-25)!}(2^{-50}) = 0.11275$

But if I do a problem like this, I get the "OVERFLOW" error on my calculator and I can't do it:

If you flip a coin 100 times, what is the chance you will get 50 heads?
$\displaystyle \frac{n!}{h!(h-n)!}(2^n)$

$\displaystyle \frac{100!}{50!(100-50)!}(2^{-100}) = ?$

Is there another way to calculate the answer for the second problem so I don't get "OVERFLOW" in my calculator every time I try to do it?

2. Originally Posted by Cursed
I keep getting an error every time I try to do calculations with large numbers. I was wondering if there was another way to do these problems or a way to simplify them. As you can see, with smaller numbers I can put them into my calculator and get an answer:

If you flip a coin 50 times, what is the chance you will get 25 heads?

$\displaystyle \frac{n!}{h!(h-n)!}(2^n)$

$\displaystyle \frac{50!}{25!(50-25)!}(2^{-50}) = 0.11275$

But if I do a problem like this, I get the "OVERFLOW" error on my calculator and I can't do it:

If you flip a coin 100 times, what is the chance you will get 50 heads?
$\displaystyle \frac{n!}{h!(h-n)!}(2^n)$

$\displaystyle \frac{100!}{50!(100-50)!}(2^{-100}) = ?$

Is there another way to calculate the answer for the second problem so I don't get "OVERFLOW" in my calculator every time I try to do it?
Which calculator are you using?

Try looking for a button which says $\displaystyle \boxed{\text{nCr}}$

My humble Casio fx-82ES is capable of calculating it that way. (But not the other more elaborate way that you are using.)

So if you use my way you will type:

$\displaystyle \boxed{\text{100}} \ \boxed{\text{nCr}} \ \boxed{\text{50}}$

Note: You might have to press $\displaystyle \boxed{\text{Shift}}$ or $\displaystyle \boxed{\text{2nd}}$ to access $\displaystyle \boxed{\text{nCr}}$