What is the expected value?

Question

If you throw exactly two heads in two tosses of a coin you win $48 dollars. If not you pay me $20.

Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

Since the possible outcomes of flipping a coin two times are {HH, HT, TH, and TT}, there is a 25% chance you will flip two heads and a 75% chance you will not flip two heads.

Therefore, the expected value would be:

0.25(48) + 0.75(-20) = 12 - 15 = -3,

so you would expect to lose $3 each time you flip two coins.