CONDITIONING AND EVIDENCE A hat contains 100 coins, where at least 99 are fair, but there may be one that is double-headed (always landing Heads); if there is no such coin, then all 100 are fair. Let...

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CONDITIONING AND EVIDENCE
A hat contains 100 coins, where at least 99 are fair, but there may be one that is double-headed (always landing Heads); if there is no such coin, then all 100 are fair. Let D be the event that there is such a coin, and suppose that P(D) = 1/2. A coin is chosen uniformly at random. The chosen coin is ?ipped 7 times, and it lands Heads all 7 times. (a) Given this information, what is the probability that one of the coins is doubleheaded? (b) Given this information, what is the probability that the chosen coin is doubleheaded?

Answered Same DayDec 26, 2021

Answer To: CONDITIONING AND EVIDENCE A hat contains 100 coins, where at least 99 are fair, but there may be one...

David answered on Dec 26 2021

124 Votes

Given,
P(Doubleheaded coin) = P(D) = 1/2
P(No Doubleheaded coin) = P(Dc) = 1 – 1/2 = 1/2
P(7 consecutive heads | Doubleheaded coin) = P(7H | D) = 1
P(7 consecutive heads | No doubleheaded coin) = P(7H | Dc) = 1/27 = 1/128
a) From the given information,
P(One of the coins is...

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CONDITIONING AND EVIDENCE A hat contains 100 coins, where at least 99 are fair, but there may be one that is double-headed (always landing Heads); if there is no such coin, then all 100 are fair. Let...

Answer To: CONDITIONING AND EVIDENCE A hat contains 100 coins, where at least 99 are fair, but there may be one...

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