Question

A fair coin is flipped 20 times.

a. Determine the probability that the coin comes up tails exactly 15 times.

b. Find the probability that the coin comes up tails at least 15 times.

c. Find the mean and standard deviation for the random variable X giving the number of tails in this coin flipping problem.

Answer 1

The binomial distribution is used to model the number of success x in n trials of an experiment with the probability of success being p.

For a fair coin, the probability of getting tails = 0.5 = p

Also n = 20

a) The probability that the coin comes up tails exactly 15 times = B(15: 20, 0.5) = = 0.0148

b) The probability that the coin comes up tails at least 15 times = = 0.014786 + 0.004621 + 0.001087 + 0.000181 + 0.000019 + 0.000001 = 0.020695 ~ 0.0207

c) The mean of binomial distribution with parameters n and p is np and it's variance is np(1-p).

Mean = np = 20*0.5 = 10

Variance = np(1-p) = 20*0.5*0.5 = 5

Standard deviation = = = 2.236

Therefore the mean number of tails in this coin flipping problem is 10 and it's standard deviation is 2.236