You are given 8 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means that you win $8 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game . Round to the nearest cent
To calculate the expected value, we need to multiply the potential outcomes by their respective probabilities.
In this case, the probability of tossing 3 tails in 3 tosses of a fair coin is (1/2)^3 = 1/8.
Since you win $8 if you succeed and lose $1 if you fail, the potential outcomes are $8 and -$1, and their respective probabilities are 1/8 and 7/8.
Now we can calculate the expected value:
Expected value = (Potential outcome 1 * Probability 1) + (Potential outcome 2 * Probability 2)
= ($8 * 1/8) + (-$1 * 7/8)
= $1 - $0.875
= $0.125
Therefore, the expected value of the game to you is $0.13 (rounded to the nearest cent).