## ParthKohli 3 years ago If 100 coins are tossed, what is the probability that exactly 50 heads will be showing?

1. ParthKohli

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

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.

3. Mimi_x3

Binomial Probability?

4. ParthKohli

I am not sure.

5. Mimi_x3

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

6. ParthKohli

Hmm, but could you possibly explain that a little?

7. 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 $$\frac{1}{2}$$

8. eliassaab

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

9. ParthKohli

Oh, yes! How could I forget combinations?!

10. eliassaab

11. Mimi_x3

woops..but am i wrong?

12. ParthKohli

Now I really feel silly.

13. ParthKohli

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

14. eliassaab

yw

15. Mimi_x3

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

16. Mimi_x3

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

17. eliassaab

Mimi, you are right.

18. 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?

19. eliassaab

You can think about one coin tossed 100 times.

20. Mimi_x3

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

21. eliassaab

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

22. Mimi_x3

ok. i got it. thanks.