If a clean coin is tossed 1,000 times, what is the probability that you will get exactly 500 heads and 500 tails. Show your calculations and thank you for any help.
The probability of 500 heads = probability of 500 tails
Out of 1000 flips, we want any 500 of them to be heads = C(1000, 500)
Probability of heads on any 1 toss = 1/2 = probabiliy of tails on any one toss
So, we have
C(1000,500) * (1/2)^500 * (1/2)^500 = about .025 = about 2.5%
The probability of 500 heads = probability of 500 tails
Out of 1000 flips, we want any 500 of them to be heads = C(1000, 500)
Probability of heads on any 1 toss = 1/2 = probabiliy of tails on any one toss
So, we have
C(1000,500) * (1/2)^500 * (1/2)^500 = about .025 = about 2.5%