If a fair coin is tossed 9 times, what is the probability, to the nearest thousandth, of getting exactly 3 tails?

Answer 1

nCr[(p)^n(q)^n-r]

n=9, r=3, p=1/2 = q,

9 flips, 3 tails, 1/2 chance of heads, 1/2 chance of tails

= 9C3(1/2)^3(1/2)^6

= 9!/3!6!(1/8)(1/64)

= 9x8x7/3x2(1/8x64)

= 84/8x64

= 21/128

= 0.1640625

= 16.40625%

= 16.406% rounded off to nearest thousandth

Probabilities of exact number of tails, from 0 to 9 in 9 flips

Pr(0 tails) = 1/512 = Pr(9 tails) = .001953125 = 0.195%

Pr(1 tail) = 9/512 = Pr(8 tails) = .017578125= 1.756%

Pr(2 tails) = 36/512 = Pr(7 tails)= .0703125 = 7.031%

Pr(3 tails) = 84/512 = Pr(6 fails)= .1640625 =16.406% = probability of exactly 3 tails in 9 flips of a fair coin

Pr(4 tails) = 126/512 = Pr(5 tails)= .24609375 = 24.609%

2(.195 + 1.756 + 7.031 + 16.406 + 24.609) = 100%