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 $5. if kyd selects any other type of card, he pays north $2. a) what is kyd's expected value for this game? b) what is north's expected value for this game? c) who has the advantage in this game?

Step-by-step explanation:

In a 52 deck, there are 12 face cards (4 Jacks, 4 Queens, and 4 Kings).  The remaining 40 cards are non-face cards.

The probability that Kyd draws a face card is 12/52, and the probability that he draws a non-face card is 40/52.

a) Kyd's expected value is:

K = (12/52)(5) + (40/52)(-2)

K = -5/13

K ≈ -$0.38

b) North's expected value is:

N = (12/52)(-5) + (40/52)(2)

N = 5/13

N ≈ $0.38

c) Kyd is expected to lose money, and North is expected to gain money.  North has the advantage.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)