According to your roommate, they have inherited a special coin from their great-grandmother which is “magic" and "comes up heads WAaAaAaY more often than it comes up tails". You give your roommate the benefit of the doubt, and will devise a hypothesis test to try and support their claim that the coin is biased in favor of heads. (a) What is a sensible choice for a null and alternative hypothesis for this test? (b) If you are only able to flip the coin 10 times, and will only conclude that the coin is biased if all 10 flips come up heads, what is the probability of a Type I error for this test? Use exact Binomial probabilities.

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A: I am attaching image so that you understand each and every step.

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A:

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A:

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A: We have given that p(a)= 0.40  p(b) = 0.20  p(b|a)= 0.30 p(a|b) = ?

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