Ask a question... to determine if a coin is fair, it is flipped 50 times and the

Question

Ask a question...

to determine if a coin is fair, it is flipped 50 times and the number of heads is recorded. If the number of heads is within 5 of the expected number of heads (25) then the coin is judged to be fair. that is a coin is judged to be fair if the number of heads in 50 flips is at leats 20 and at most 30.

A) suppose that the coin is actually fair so that it will land on haeds 50% of the time in the long run.What is theprobability that itwill mistakenly be declared "not fair" according to this criterion?

B)suppose that you cahnged the criterion so that a coin is judged to be fair if the number of heads in 50 flips is within k of the expected number of heads. I fyou wanted to reduce the probability of the error described in part (a) to less than 1% what is the smallest value k you can use? justify

c) suppose that a different coin is biased so that it willl land on heads 60% of the time. What is the probability that it will mistakenly be declared "fair" according to the original criterion?

D) how would the probability in part (C) change if the coin will land on heads 70% of the time? explain why this makes sense.

Explanation / Answer

There are only two possible outcomes: Either both heads and tails come out an even number of times, or they both come out an odd number of times. This is so because if heads came up x times and tails came up y times then x+y=100, and the even number 100 can't be the sum of an even and an odd number. A good way to solve this problem is to notice that if we have a sequence of 100 coin tosses in which tails came up an odd number of times, than by flipping the result of the first toss you get a sequence where tails came up an even number of times (and no matter what came up in the first toss!). Hence you have a bijection between the set of sequences where tails occurs an odd number of times, and the set of sequences where tails occurs an even number of times.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.