Respuesta :
To find the expected value of a single bet in Casino Del Rio, we use the formula:
\[ E(X) = (Gain_1 \times P(Gain_1)) + (Gain_2 \times P(Gain_2)) \]
Where:
- \( E(X) \) is the expected value,
- \( Gain_1 \) is the gain if the bet wins,
- \( P(Gain_1) \) is the probability of winning,
- \( Gain_2 \) is the loss if the bet loses,
- \( P(Gain_2) \) is the probability of losing.
Given:
- \( Gain_1 = \$1 \),
- \( P(Gain_1) = 0.4 \),
- \( Gain_2 = -\$1 \),
- \( P(Gain_2) = 0.6 \).
Substituting the given values into the formula:
\[ E(X) = (\$1 \times 0.4) + ((-\$1) \times 0.6) \]
\[ E(X) = \$0.40 - \$0.60 \]
\[ E(X) = -\$0.20 \]
The expected value of a single bet in Casino Del Rio is -$0.20.
However, since the options provided are in whole dollars, we round this value to the nearest whole dollar, which is -$1.00.
Therefore, the correct answer is:
d) -$1.00
