Question

A biased coin has a probability of 0.4 of coming up heads. What is the probability that when flipped one hundred times it comes up heads half of the trials or more. Give answer to at least three decimal points.

Answer 1

Using the binomial probability relation ; the probability that an head is obtained at least 50 times is 0.0271

Using the binomial probability relation :

• P(x = x) = nCx * p^x * q^(n-x)
• p = probability of success = 0.4
• q = 1 - p = 0.6
• n = number of trials = 100

P(x ≥ 50) = p(x = 50) + p(x = 51) + ...+ p(x = 100)

Using a binomial probability calculator :

P(x ≥ 100) = 0.0271

Therefore, the probability that atleast 50 heads are obtained in the trial is 0.0271

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