a) One of two boxes contain 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2. A box is selected at random and a ball is selected at random from it. a) Given that the ball selected is red, what is the probability it was selected from the first box? b) Given that the ball selected is red, what is the probability it was selected from the second box? c) Compare the results in parts a) and b) and explain the answer.

Answer:

The answer is below

Step-by-step explanation:

Let B₁ represent box 1, B₂ represent box 2, E₁ represent the event of selecting box 1, E₂ represent the event of selecting box 2 and R represent the event of selecting a red ball.

Given that:

Probability of selecting box 2 P(E₂) = 2/3, Probability of selecting box 1 = P(E₁) = 1/3

Probability of selecting red ball from box 1 = P(R | E₁) = 4/6 [4 red balls out of 4 red, 2 green]

Probability of selecting red ball from box 2 = P(R | E₂) = 2/6 [2 red balls out of 2 red, 4 green]

a)

Given the ball is red, the probability it was selected from the first box is:

[tex]P(E_1|R)=\frac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)} =\frac{2/3*1/3}{(2/3*1/3)+(1/3*2/3))} =\frac{1}{2}[/tex]

b)

Given the ball is red, the probability it was selected from the second box is:

[tex]P(E_2|R)=\frac{P(R|E_2)P(E_1)}{P(R|E_2)P(E_2)+P(R|E_1)P(E_1)} =\frac{1/3*2/3}{(1/3*2/3)+(2/3*1/3))} =\frac{1}{2}[/tex]

c)

We can see that both probabilities are equal. Although we have more red balls in box 1 (twice as much) than in box 2 but the probability of selecting from box 2 (is twice as much) than from selecting from box 1.

The probability that the ball selected is red and it is selected from the first box is 1/2 and the probability that the ball selected is red and it is selected from the second box is 1/2.

Given :

a) The probability that the ball selected is red and it is selected from the first box is:

[tex]P(E_1|R)=\dfrac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]

[tex]P(E_1|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]

[tex]P(E_1|R)=\dfrac{1}{2}[/tex]

b) The probability that the ball selected is red and it is selected from the second box is:

[tex]P(E_2|R)=\dfrac{P(R|E_2)P(E_2)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]

[tex]P(E_2|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]

[tex]P(E_2|R)=\dfrac{1}{2}[/tex]

c) The probability that the ball selected is red and it is selected from the first box and the probability that the ball selected is red and it is selected from the second box is the same.

For more information, refer to the link given below:

https://brainly.com/question/795909

-0.1 = -10e e= i need this asap

What is the value of m in the diagram?
A. 11.2
B. 20.02
C. 15.8
D. 11

HELPP PLEASEEEEEEEEEE WILL GIVE BRAINLIST

Help please!!!!!!!!!!

100% is shown on the following tape diagram.
?
100%
What percent is represented by the entire tape diagram?
%

Someone pls HELP RN IM IN A HURRY

HELP !!!! A rental car company charges $61 per day to rent a car and $0.12 for every mile driven. Nathan wants to rent a car, knowing that: • He plans to drive 400 miles. • He has at most $170 to spend.​

A behavioral economist studies transportation habits in an urban center. She identifies 4 bus routes that connect to 3 different light rail routes available to participants in the study. Before she interviews participants, she must determine the number of possible routes participants can choose to use. Which expression represents the number of available options

a. 4!+3!
b. 4×3
c.4!×3!
d. 4!/3!

The scale on a map reads 2 inches = 125 miles.
If two cities are 4 inches apart on the map.
what is their actual distance?

Three people go out to lunch. They decide
to share the $69.00 bill evenly. How much
does each person pay?

is this right? and if not pls tell why but if I'm right tell why anyway​

What is the area of rhombus ABCD?



Enter your answer in the box. Do not round at any steps.

[ ] units²

write another way to add these numbers using the associative property and then state the sum.
(40+7)+13​

Morris started work today at 7 a.m. and worked until 4:30 p.m. He earns $12 per hour for his regular shift, which is 8 hours, and 50% more per hour for overtime. How much money did Morris make today?

If an airplane pilot was told to rotate his plane while he was flying to Honolulu, would that be enough information for her to know what to do? Explain.

Pls help me in one question in math

5x+7 y=-19 y=-3x-21
find x and y please show your work.

Let a =[2,4,6] b=[3,7,10,13] and c= [3,4,6,7,10,13] Which of the following is true
a. Set A is Subset of Set C
b. Set B is Subset of Set C
c. Both a and b is Subset of Set C
d set B is Subset of Set a

Prove whether the following inferences are valid using the long or short truth table method. If they are invalid, give the counterexample.
A > -B |= B > -A​

(-1) + 1 = 0 is which inverse​

Here are the ages of 14 adults.

42
35
56
39
40
51
47
38
42
55
42
48
49
41

Draw an ordered stem and leaf diagram for these ages.

PLS HELP i need this badddd

Solve and show your work
What is the work
formula?
Kevin delivers 30newspapers in 2 hours. How many newspapers can be
deliver in 3 hours? Find the unit rate first to solve this two-step problem

Amanda is calculating how many seats there are in Wembley Stadium in London, England. She counts that there are 3,750 rows. Each row has 24 seats. How many seats are there in the whole stadium?

Two coaches and two mathletes wish to cross a river. They make a raft but it will only carry the weight of 1 coach or 2 mathletes (1 coach and 1 mathlete is too much; 1 mathlete is just fine). What is the minimum number of times the raft must cross the river to get all four people to the other side? (Note: the raft can not cross the river if it’s empty - you need at least one person on it!)

In a class book order, 2/3 of the books are fantasy and 1/4 of the books are biography. If the order contains 60 books, how many books are either fantasy or biography?

Ryan wrote a number on his paper. His number rounds to 350 when rounded to the nearest ten. His number rounds to 300 when rounded to the nearest hundred. Enter a number that Ryan could have written.

What is the correct solution to the
inequality?

cupcakes for a bake sale. He can bake 45
cupcakes in one hour. Which inequality shows the minimum number of hours that Hannah must bake to make at least 250
cupcakes?

What is 1 1/3 - 3/4=?