Respuesta :
Answer:
a) -0.1536
b) 0.1536
c) North has the advantage in this game
Step-by-step explanation:
We can calculate the probability as:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P(Face card) =
[tex]=\dfrac{12}{52} = 0.2308[/tex]
P(Non-face card) =
[tex]=\dfrac{40}{52} = 0.7692[/tex]
" If Kyd selects a face card, North pays him $6. If Kyd selects any other type of card, he pays North $2."
a) Kyd's expected value for this game
We can write the probability distribution for Kyd as:
Event: Face Card Non-face Card
x: +6 -2
P(x): 0.2308 0.7692
[tex]E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = +6(0.2308) + (-2)(0.7692)\\E(x) = -0.1536[/tex]
Expected value for Kyd is -0.1536
b) North's expected value for this game
We can write the probability distribution for North as:
Event: Face Card Non-face Card
x: -6 +2
P(x): 0.2308 0.7692
[tex]E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = -6(0.2308) + (2)(0.7692)\\E(x) = 0.1536[/tex]
Expected value for North is 0.1536
c) Thus, North has the advantage in this game as the expected value for North is greater than the expected value for Kyd.
