Question

If an unfair coin is tossed into the air and drops without interruption, its probability of landing on heads is 0.51 whereas the probability of landing on tails is 0.49. If the payoff for landing on heads is $0.99 and the payoff for landing on tails is $1.01 and it costs $1 to play each game, should you play?

1)Yes, because over the long run your expected value is greater than the lowest payoff

2)No, because over the long run your expected value is lower than the lowest payoff

3)Yes, because over the long run your expected value is greater than the cost to play

4)No, because over the long run your expected value is less than the cost to play

Answer 1

4) No, because over the long run your expected value is less than the cost to play

Explanation:

The expected value is ...

0.51×0.99 + 0.49×1.01 = 0.5049 +0.4949 = 0.9998

This expected value is less than the cost to play, so you will lose money in the long run. You should not play.