Question

What is the probability that a fair coin lands tails up ten times in a row?

Answer 1

Answer

This is a case of binomial distribution with n = 10 and p = 0.5 (because there is 1/2 or 0.5 probability of getting a tails)

using the binomial formula

P(x=r) = C(n,r)*p^r*(1-p)^{n-r)

setting n = 10, r = 10 and p = 0.5

we get

P(x=10) = C(10,10)*0.5^10*(1-0.5)^{10-10}

={10!/((10-10)!*10!}*0.5^10*0.5^0

= 1*0.5^10*1

= 0.00098

= 0.0010 (rounded to 4 decimals)