SOLUTION: You are given 12 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value(to y
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-> SOLUTION: You are given 12 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value(to y
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Question 325274: You are given 12 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value(to you) of the game. Round to the nearest cent. Answer by solver91311(24713) (Show Source):
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The probability of successes in trials where the probability of success on any given trial is is given by:
where is the number of combinations of things taken at a time and is computed using
For this problem, given a fair coin, the probability of success on any given trial is , and you want 3 successes out of 3 trials, hence:
You can calculate this for yourself. Hint: and anything to the zero power is 1.
That gives you the probability of winning. The probability of losing is .
The expected outcome is the amount you lose whenever you lose times the probability of losing plus the amount you win whenever you win times the probability of winning.
