Mathematics, 18.04.2020 03:47 hi510hello

Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $2. Round to the second decimal place.

a) What is Kyd's expected value for this game? Round your answer to the nearest cent. $
b) What is North's expected value for this game? Round your answer to the nearest cent. $
c) Who has the advantage in this game?

Answers: 3

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Answer from: makayla4141

a) -0.1536

b) 0.1536

c) North has the advantage in this game

Step-by-step explanation:

We can calculate the probability as:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

P(Face card) =

$=\dfrac{12}{52} = 0.2308$

P(Non-face card) =

$=\dfrac{40}{52} = 0.7692$

" 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

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = +6(0.2308) + (-2)(0.7692)\\E(x) = -0.1536$

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

$E(x) = \displaystyle\sum x_iP(x_i)\\E(x) = -6(0.2308) + (2)(0.7692)\\E(x) = 0.1536$

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.

Answer from: Quest

10a^3+277a^2-132a-792

step-by-step explanation:

(2a+11)(5a-12)(foil)

=10a^2-24a+55a-132 =10a^2+31a-132

(10a^2+31a-132)(a+6)

=10a^3+60a^2+31a^2+186a^2-132a-792 =10a^3+277a^2-132a-792

i hope this is what you are looking for : )

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

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Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects...