Bill claims that he has a coin which is biased and which comes up heads more than tails.His claim is based on a trial in which he flipped the coin 200 times and got 110 heads.If the coin were actually fair,what would be the probability of getting 110 or more heads?
A)0.579
B)0.421
C)0.079
D)0.059
E)0.921

Question

Quizplus · Accepted Answer

If the coin were fair, the probability of getting heads on any given flip would be 0.5. Using the binomial distribution, we can calculate the probability of getting 110 or more heads in 200 flips with a success probability of 0.5.

P(X ≥ 110) = 1 - P(X ≤ 109)

P(X ≤ 109) = Σ(k=0 to 109) [(200 choose k) * 0.5^200] = 0.921

P(X ≥ 110) = 1 - 0.921 = 0.079

Therefore, the probability of getting 110 or more heads if the coin were fair is 0.079, which is closest to choice C.

Bill Claims That He Has a Coin Which Is Biased