Suppose you have two urns with poker chips in them. Urn I contains two red chips and four white chips. Urn II contains three red chips and one white chip. You randomly select one chip from urn I and put itinto urn II. Then you randomly select a chip from urn II. What is the probability that the chip you select from urn II is red?

Step-by-step explanation:

Step 1: Understanding the possible events

Selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be completed in two ways:

A. Selecting a red chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II

B. Selecting a white chip from Urn I and adding it to Urn II and then selecting a red chip from Urn II

Therefore total probability is:

Step 2: Probability of selecting either chip from Urn I

Urn I contains 2 reds and 4 white chips, that gives a total of 6 chips.

Step 3: Probability of selecting a red chip from Urn II

Urn II originally contains 3 reds and 1 white chip, that gives a total of 4 chips.

Remember: Once a chip is added from Urn I to Urn II the total number of chips will increase in the Urn II

Case 1: When a red chip is added from Urn I to Urn II

Red chips    = 4

White chips = 1

Total Chips  = 5

Case 2: When a white chip is added from Urn I to Urn II

Red chips    = 3

White chips = 2

Total Chips  = 5

Therefore the total Probability of selecting a chip from Urn I and then adding that chip to Urn II and then selecting a red chip from Urn II can be calculated as:

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24