You are given 4 to 3 odds against tossing three heads with three coins, meaning you win $4 if you succeed and you lose $3 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. Find the expected value (to you) for the game.

Solution:

game outcomes and their values

game outcomesvalue

HHH+ 5

HHT-1

HTH-1

HTT-1

THH-1

THT-1

TTH-1

TTT-1

expected value = 5 * P(HHH) - 1 * P(HHT) -  1 * P(HTH)  -  1 * P(HTT)  -  1 * P(THH)  -  1 * P(THT)  -  1 * P(TTH)  -  1 * P(TTT)

                      = 5 * 1/8 - 1 * 7/8

                      = - 2/8

                      = - 1/4

the outcome of 1 game cannot be predicted; but if you play, say, 100 games you can expect to lose about a quarter per game, i.e. over a hundred games you would lose about  $25.

Step-by-step explanation:

Hope this helped

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Thanks for the points also.

the diver is 33 feet below the surface.

step-by-step explanation:

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