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On three rolls of a single​ die, you will lose ​$12 if a 4 turns up at least​ once, and you will win ​$7 otherwise. What is the expected value of the​ game?

User ZedBee
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1 Answer

4 votes

Final answer:

The expected value of the game is $3.96.

Step-by-step explanation:

The expected value of a game is calculated by multiplying each possible outcome by its probability and summing the results.

In this case, there are two outcomes: losing $12 if a 4 appears at least once, and winning $7 otherwise.

Probability of getting a 4 at least once: 1 - Probability of not getting a 4 three times

= 1 - (5/6) * (5/6) * (5/6)

= 1 - (125/216)

= 91/216

Amount lost when a 4 appears at least once: -$12

Probability of not getting a 4 at all:

(5/6) * (5/6) * (5/6)

= 125/216

Amount won when a 4 does not appear at all: $7

Expected value = (Probability of losing * amount lost) + (Probability of winning * amount won)

= (91/216 * -$12) + (125/216 * $7)

= -$4.22 + $8.18

= $3.96

Therefore, the expected value of the game is $3.96.

User Greenthunder
by
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