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Conditional Probability: Fair and unfair coin?

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A box contains 5 fair coins and 5 biased coins. Each biased coin has a probability of a head 4/5. A coin is drawn at random from the box and tossed. Then a second coin is drawn at random from the box (without replacing the first one.)

Given that the first coin has shown head, What is the probability of second coin is fair?

posted Jul 20, 2017 by anonymous

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Let us suppose you chose the sequence to be: H T H
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The results of the game 1 toss:
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The results of the game 2 toss:
You: T T H T T H H T H
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The results of the game 3 toss:
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Now after 3 games, your average score is 7 and your friend’s average score is 8. Now assume that you keep playing the game and play many times. What will be the possible outcome of the following?

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A standard dice has the numbers 1 to 6, each appearing with a probability of (1/6).
If the dice is modified so the number 6 appears half the frequency of the other numbers, what is the new probability of rolling a 6 ?

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