If 100 coins are tossed, what is the probability that exactly 50 heads will be showing?

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- ParthKohli

If 100 coins are tossed, what is the probability that exactly 50 heads will be showing?

- schrodinger

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- ParthKohli

Is this as simple as saying "1/2"?

- ParthKohli

Since I found this from the 50 Hard Probability Problems webpage(http://www.delphiforfun.org/Programs/Math_Topics/FiftyProbabilityProblems.htm), I think there is something tricky going on there.

- Mimi_x3

Binomial Probability?

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## More answers

- ParthKohli

I am not sure.

- Mimi_x3

100C50 * (1/2)^{50} * (1/2)^{50}

- ParthKohli

Hmm, but could you possibly explain that a little?

- Mimi_x3

\[\tbinom{100}{50} *\left(\frac{1}{2}\right)^{50}*\left(\frac{1}{2}\right)^{50} = 0.0796\]
\(p=q= \frac{1}{2}\) This is a particular case of probability of binomial probability when probabilities \(p\) and \(q\) of successes and failure are both \(\frac{1}{2}\)

- anonymous

You have to get 50 heads and 50 tails the probability of that is
\[
\frac 1 {2^{50}}\frac 1 {2^{50}}
\]
There are
\[
100C50
\]
such possiblities

- ParthKohli

Oh, yes! How could I forget combinations?!

- anonymous

The answer is about .08

- Mimi_x3

woops..but am i wrong?

- ParthKohli

Now I really feel silly.

- ParthKohli

Thank you @eliassaab @Mimi_x3
Mimi, I might not be a qualified person to judge that. :p

- anonymous

yw

- Mimi_x3

@eliassaab: I have a question..I don't think I'm wrong..this looks like Binomial Probability..

- Mimi_x3

wait forget it i read the question wrongly..100 coins are tossed..not 100 coins are tossed 100 times..sorry.

- anonymous

Mimi, you are right.

- Mimi_x3

I'm sorry; but I'm confused I'm not that good with Probability.
Re-reading the question again it says "100 coins are tossed" does that mean that it's not Binomial Probability? Since it is not 100 times?

- anonymous

You can think about one coin tossed 100 times.

- Mimi_x3

But 100 coins are tossed; does that mean it is all tossed at the same time? So it is not Binomial Probability.

- anonymous

Tossing 100 coins and tossing a coin 100 times is the same event.

- Mimi_x3

ok. i got it. thanks.

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