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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (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:



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.


John