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3. Sum rule for conditional probability Let’s assume there is 1 fake coin out of 1000...

3. Sum rule for conditional probability

Let’s assume there is 1 fake coin out of 1000 coins. ( P[Coin=fake] = 0.001 ) The probability of showing head for fake coin is 0.9 (P[Head | Coin=fake] = 0.9). For normal coin, the probability of showing head is 0.5 (P[Head | Coin=normal] = 0.5). If you have a coin and toss it, what is the probability that you will get a head and the coin is fake (P[Head & Coin=fake])? What is the probability that you will get a head and the coin is normal (P[Head & Coin=normal])?    

For the coin in problem 3, if you have a coin, what is the probability that you will get a head, P[Head]?  

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