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

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Is this as simple as saying "1/2"?
Since I found this from the 50 Hard Probability Problems webpage(, I think there is something tricky going on there.
Binomial Probability?

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I am not sure.
100C50 * (1/2)^{50} * (1/2)^{50}
Hmm, but could you possibly explain that a little?
\[\tbinom{100}{50} *\left(\frac{1}{2}\right)^{50}*\left(\frac{1}{2}\right)^{50} = 0.0796\] \(p=q= \frac{1}{2}\) This is a particular case of probability of binomial probability when probabilities \(p\) and \(q\) of successes and failure are both \(\frac{1}{2}\)
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
Oh, yes! How could I forget combinations?!
The answer is about .08
woops..but am i wrong?
Now I really feel silly.
Thank you @eliassaab @Mimi_x3 Mimi, I might not be a qualified person to judge that. :p
@eliassaab: I have a question..I don't think I'm wrong..this looks like Binomial Probability..
wait forget it i read the question wrongly..100 coins are tossed..not 100 coins are tossed 100 times..sorry.
Mimi, you are right.
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?
You can think about one coin tossed 100 times.
But 100 coins are tossed; does that mean it is all tossed at the same time? So it is not Binomial Probability.
Tossing 100 coins and tossing a coin 100 times is the same event.
ok. i got it. thanks.

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