Question

If you throw exactly three heads in six tosses of a coin you win $23. If not, you pay me $10. 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

probability of getting a heads on single flip (p) = 1/2 = 0.5

number of trials n = 6 and we have to find P(X=3)

So, there is 0.3125 probability of getting exactly 3 heads, i.e. winning $23

there is 1-0.3125 = 0.6875 probability of not getting exactly 3 heads, i.e. losing $10

Expected value = $23*0.3125 - $10*0.6875

E[x] = $7.1875 - $6.875

E[x] = $0.31 (2 decimals)