Question: Consider the problem of determining whether a coin is a fair one,i.e., P(heads)=P(tails)=0.5, by flipping the coin 10 times. Use the binomial theorem and basic

Consider the problem of determining whether a coin is a fair one,i.e., P(heads)=P(tails)=0.5, by flipping the coin 10 times. Use the binomial theorem and basic probability to answer the following questions.

a) A coin is flipped ten times and it comes up head every time, What is the probability of getting 10 heads in a row and what would you conclude about whether the coin is fair?

b) Suppose 10,000 coins are each flipped 10 times in a row and the flips of 10 coins result in all heads, can you confidently say that these coins are not fair?

c) What can you conclude about results when evaluated individual versus in a group?

e) Suppose that you flip each coin 20 times and then evaluate 10,000 coins. Can you now confidently say that any coin which yields all heads is not fair?

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