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): You can put this solution on YOUR website!
The probability of 
successes in 
trials where the probability of success on any given trial is 
is given by:
\ =\ \left(n\cr{k}\right)\left(p\right)^k\left(1\ -\ p\right)^{n\,-\,k})
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:
\ =\ \left(3\cr{3}\right)\left(\frac{1}{2}\right)^3\left(\frac{1}{2}\right)^{0})
You can calculate this for yourself. Hint: \ =\ 1)
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.
John
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