Question

You are given 3 to 2 odds against tossing three heads with three? coins, meaning you win ?$3 if you succeed and you lose ?$2 if you fail. Find the expected value? (to you) of the game. Would you expect to win or lose money in 1? game? In 100? games? Explain.

Answer 1

The probability of tossing 1 head is = 1/2; The probability of tossing 3 heads with 3 coins = (1/2)³ = 1/8;

So, expected value of the game = P(success) * Value of success + P(Failure) * Value of failure
= 1/8 * 3 + (1-1/8) * (-2) = 3/8 + 7/8 (-2) = 3/8 - 14/8 = -11/8;
Thus, the expected value of the game is negative i.e. = -1.38$
Thus, it is expected that money will be lost in 1 game equivalent to 1.38$;

In a 100 games too, this expected loss of money will further increase and will become 100*1.38 = 137.5$;