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Probabilities

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See attached file for complete problem set.

1. Find the probability of obtaining three heads.
2. What is the probability that he will be at his starting point after three flips of the quarter?
3. What is the expected number of 1's?
4. What is the standard deviation of the number of 2's?

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Solution Summary

The expert examines the probability in coin tosses. Fair die rolling is analyzed.

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If you pick the two headed coin, you have a 100% probability of getting three heads. For the other two coins, you have a (0.5)(0.5)(0.5) = 0.125 = 12.5% probability of getting three heads.
So the probability that you get three heads with a randomly chosen coin is:
P = probability of choosing two-headed coin * probability of three heads + probability of choosing one-headed coin * probability ...

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