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There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random. 1) What is the probability that the marble is blue? 2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each? Make sure to clearly define your probabilistic events and mathematically show how different probability laws and rules that you learned in class could be applied to solve the problems.

Answers

Answer 1

Answer:

0.4 ; 0.6125

Step-by-step explanation:

Given the following :

Bag 1 : 75 red ; 25 blue

Bag 2: 60 red ; 40 blue

Bag 3: 45 red ; 55 blue

Probability = (required outcome / Total possible outcomes)

A) since the probability of choosing each bag is equal :

BAG A:

P(choosing bag A) = 1 / total number of bags = 1/3 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (1/3 × 75/100) = 25/300

BAG B:

P(choosing bag B) = 1/3 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (1/3 × 40/100) = 40/300

BAG C:

P(choosing bag C) = 1/3

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (1/3 × 55/100) = 55/300

= (25/300) × (40/300) × (55/300) = (25 + 40 + 55)/300 = 120/300 = 0.4

2) What is the probability that the marble is blue when the first bag is chosen with probability 0.5 and other bags with equal probability each?

BAG A:

P(choosing bag A) = 0.5 ; P(choosing blue marble) = number of blue marbles / total number of marbles = 25/100

HENCE, choosing a blue marble from bag A : = (0.5 × 75/100) = (0.5 * 0.75) = 0.375

BAG B:

P(choosing bag B) = (1-0.5) / 2 = 0.25 ;

P(choosing blue marble) = number of blue marbles / total number of marbles = 40/100

HENCE, choosing a blue marble from bag A : = (0.25 × 40/100) = (0.25 × 0.4) = 0.1

BAG C:

P(choosing bag C) = (1 - (0.5+0.25)) = 0.25

P(choosing blue marble) = number of blue marbles / total number of marbles = 55/100

HENCE, choosing a blue marble from bag A : = (0.25 × 55/100) = 0.25 × 0.55 = 0.1375

= 0.1375 + 0.1 + 0.375 = 0.6125

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B. It must be greater than or equal to 6 and at most 24.
C. It must be greater than 6 and less than 24.
D. It must be greater than 6 and at most 24.

Answers

Your answer is B
As the sum of any 2 lengths of a triangle is always greater than the third length

Hope it helps ♥

Answer: Its C

Step-by-step explanation: Just took unit test

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Answers

Answer:

Check pdf

Step-by-step explanation:

Which function is a quadratic function?P(x)=2x(×^2+6)+1
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t(x)=-8x^2(x^2-6+1
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Answers

The correct answer is: [D]: " H(x) = 3x(x - 2) - 4 " .
__________________________________________________
Note: A "quadratic function" takes the form of:
__________________________________________________
f(x) = ax² + bx + c ;
_________________________________________________
Answer choice: [D]: " H(x) = 3x(x - 2) - 4 " ;

takes this form:
_________________________________________________
" H(x) = 3x(x - 2) - 4 " ;

→ " 3x(x - 2) - 4 " ;

Note the "distributive property" of multiplication:
_________________________________________________

a(b + c) = ab + ac ; AND

a(b - c) = ab - ac ;
_________________________________________________

→ As such;

" 3x(x - 2) = (3x * x) - (3x * 2) = 3x² - 6x;

So, we can rewrite the expression:

→ " 3x(x - 2) - 4 " ;

as: → " 3x² - 6x - 4 ;

And the entire function as:

H(x) = 3x(x - 2) - 4 ;

as:

H(x) = 3x² - 6x - 4 ;

Which takes the form of a "quadratic function" ;

→ f(x) = ax² + bx + c ;

in which: a = 3 ; b = - 6 ; c = - 4 .
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Answers

The graph of the Equation y= 3x- 5 with coordinates (0, 5) and (1.667, 0) is attached below.

We have,

y= 3x - 5

Now, to find the coordinates to plot one the graph put the distinct value of x as

For x= 0

y= -5

then, for x= 1

y= 3 - 5

y= -2

then, for x= 2

y= 6-5

y= 1

and, for x= 3

y= 9 - 5

y= 4

Learn more about Graph here:

brainly.com/question/29189992

#SPJ2

slope intercept form is

y=mx+b

where m is the slope and b is the y intercept

the equation is given in slope intercept form so that the

slope = 3

y-intercept = -5

to graph this you will first place a point on (-5,0) since it's the y intercept.

then since the slope is rise/run and we have 3 (or 3/1) you will start at (-5,0), and from there go up 3 units and to the right one unit. where you end up will be your second point.

hope this helps

An advertising agency is estimating costs for promoting a music festival. The job will require 200 direct labor hours at a cost of $50 per hour. Overhead costs are applied at a rate of $65 per direct labor hour.1. What is the total estimated cost for this job?
2. If the company applies a markup of 20% of total costs (price quote is 120% of total costs), what price should it quote for this job?

Answers

Answer:

$23,000 and $27,600

Step-by-step explanation:

To find the total cost of the job, we do the equation: $50 x 200

This equation will calculate the cost of the direct labor.

$50 x 200 = $10,000

Now, calculate the overhead prices

The equation is 200 x $65

This equals 13,000

Now add them and you get 23,000

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Answers

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