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

Answer:

- $12.5

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 = $\ 6\times\frac{\textup{1}}{\textup{8}}-\ 1\frac{\textup{7}}{\textup{8}}$  

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