## ParthKohli Group Title If 100 coins are tossed, what is the probability that exactly 50 heads will be showing? one year ago one year ago

1. ParthKohli Group Title

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

2. ParthKohli Group Title

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 Group Title

Binomial Probability?

4. ParthKohli Group Title

I am not sure.

5. Mimi_x3 Group Title

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

6. ParthKohli Group Title

Hmm, but could you possibly explain that a little?

7. Mimi_x3 Group Title

$\tbinom{100}{50} *\left(\frac{1}{2}\right)^{50}*\left(\frac{1}{2}\right)^{50} = 0.0796$ $$p=q= \frac{1}{2}$$ 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 Group Title

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 Group Title

Oh, yes! How could I forget combinations?!

10. eliassaab Group Title

11. Mimi_x3 Group Title

woops..but am i wrong?

12. ParthKohli Group Title

Now I really feel silly.

13. ParthKohli Group Title

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

14. eliassaab Group Title

yw

15. Mimi_x3 Group Title

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

16. Mimi_x3 Group Title

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

17. eliassaab Group Title

Mimi, you are right.

18. Mimi_x3 Group Title

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 Group Title

You can think about one coin tossed 100 times.

20. Mimi_x3 Group Title

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

21. eliassaab Group Title

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

22. Mimi_x3 Group Title

ok. i got it. thanks.