Suppose that a given coin is known to be “fair” or “unbiased” (i.e., the probabi

Question

Suppose that a given coin is known to be “fair” or “unbiased” (i.e., the probability of Heads is 0.5 per toss). In an experiment, the coin is to be given n = 10 independent tosses, resulting in exactly one out of 210 possible outcomes. Rank the following five outcomes in order of which has the highest probability of occurrence, to which has the lowest.
Outcome 1: (H H T H T T T H T H)
Outcome 2: (H T H T H T H T H T)
Outcome 3: (H H H H H T T T T T)
Outcome 4: (H T H H H T H T H H)
Outcome 5: (H H H H H H H H H H)
Suppose now that the bias of the coin is not known. Rank these outcomes in order of which provides the best evidence in support of the hypothesis that the coin is “fair,” to which provides the best evidence against it.

Explanation / Answer

If the outcome is fair than the odds of heads or tails should be 50%/50% in an ideal setup. outcomes 1,2,3 have the same probability of occurring followed by outcome 4, then 5 with the least chance. to support the fairness outcome 2 shows the best "fairness", then 1,3, 4, 5

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