Question

in a certain game, a fair die is rolled and a player gains 20 points if the die shows a 6. if the die does not show a 6, the player loses 3 points. if the die were to be rolled 100 times, what would be the expected total gain or loss for the player?

Answer 1

The expected gain or loss is an illustration of mean and expected values.

The expected total gain is 83 points

The given parameters are:

• Addition of 20 points for rolling a 6
• Removal of 3 points for not rolling a 6

The probability of rolling a 6 in a fair die is 1/6.

The probability of not rolling a 6 in a fair die is 5/6.

So, the expected gain in each game is:

$\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}$

$\mathbf{E(x) = \frac{20}6 - \frac{15}6}$

Take LCM

$\mathbf{E(x) = \frac{5}6}$

$\mathbf{E(x) = 0.83}$

The number of games is 100.

So, the expected gain is:

$\mathbf{Gain = 100 \times 0.83}$

$\mathbf{Gain = 83}$

Hence, the expected total gain is 83 points

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