Question

If you throw exactly two heads in two tosses of a coin you win $101. If not, you pay me $30. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

The expected value of the proposition is $2.50.

Step-by-step explanation:

When a coin is tossed two times, the following is the sample space (S)

S = {HT,TH,TT,HH}

Using the information in the question, we can derive the following win/loss table:

S Probability Payoff

TH 1/4 -$30

HT 1/4 -$30

TT 1/4 -$30

HH 1/4 $100

The expected value (E) can now be calculated as follows:

E = Sum of (Probability * Payoff) = (1/4 * ($-30)) * (1/4 * ($-30)) * (1/4 * ($-30)) = (1/4 * $100) = ((1/4) * (-30)) + ((1/4) * (-30)) + ((1/4) * (-30)) + ((1/4) * 100) = $2.50