Question

You are given 6 to 1 odds against tossing three tails with three​ coins, meaning you win ​$6 if you succeed and you lose ​$1 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

- $12.5

Step-by-step explanation:

Data provided in the question:

Amount won against tossing 3 tails with 3 coins = $6

Amount lost if failed tossing 3 tails with 3 coins = -$1 (negative sign depicts loss)

Number of times games played = 100

Now,

The possible outcomes when 3 coins are tossed

H H H

H H T

H T H

H T T

T H H

T H T

T T H

T T T

P(tossing 3 tails with 3 coins) =
`\frac{\textup{1}}{\textup{8}}`

P(not (tossing 3 tails with 3 coins ) =
`\frac{\textup{7}}{\textup{8}}`

Expected value =
`\$6*\frac{\textup{1}}{\textup{8}}-\$1\frac{\textup{7}}{\textup{8}}`

or

Expected value =
`\frac{\$\textup{(6-7)}}{\textup{8}}`

or

Expected value =
`\frac{\$\textup{-1}}{\textup{8}}`

negative sign means there will be loss

Therefore,

for 100 games

Expected loss = 100 ×
`\frac{\$\textup{-1}}{\textup{8}}`

= - $12.5