Question

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

Answer 1

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

Answer 2

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.

Answer 3

Binomial Probability?

Answer 4

I am not sure.

Answer 5

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

Answer 6

Hmm, but could you possibly explain that a little?

Answer 7

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

Answer 8

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

Answer 9

Oh, yes! How could I forget combinations?!

Answer 10

The answer is about .08

Answer 11

woops..but am i wrong?

Answer 12

Now I really feel silly.

Answer 13

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

Answer 14

yw

Answer 15

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

Answer 16

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

Answer 17

Mimi, you are right.

Answer 18

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?

Answer 19

You can think about one coin tossed 100 times.

Answer 20

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

Answer 21

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

Answer 22

ok. i got it. thanks.