# While he was a prisoner of war during World War II, John Kerrich tossed a coin 10,000 times. He...

###### Question:

While he was a prisoner of war during World War II, John Kerrich tossed a coin 10,000 times. He got 5067 heads. If the coin is perfectly balanced, the probability of ahead is 0.5.
16. Is there reason to think that Kerrich's coin gave too many heads to be balanced? To answer this question, find the probability that a balanced coin would give 5067or more heads in 10,000 tosses. Use the Normal approximation if appropriate.
A. 0.0901
B. 0.9099
C. 0.6667
D. 0.0019
E. 0.0067
F. 0.9981
A. The probability that Kerrich got 5067 heads is very small (almost like winning the lottery), making it highly unreasonable that the coin was balanced.
B. Kerrich's result is reasonable for a balanced coin.
C. In the Normal approximation, the probability that the number of heads was exactly 5067 is zero, i.e. P(X = 5067) = 0. Thus we conclude that the coin must have beenunbalanced.
D. There is equal probability to get any number of heads between 0 and 10,000 if the coin is exactly balanced. Thus Kerrich's result does not disprove that the coinwas balanced.

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