Please show all work, step by step. A box contains 3 marbles, 1 red, 1 green, an

Question

Please show all work, step by step.

A box contains 3 marbles, 1 red, 1 green, and 1 blue. Consider an experiment that consists of taking 1 marble from the box, then replacing it in the box and drawing a second marble from the box. Describe the sample space. Repeat when the second marble is drawn without first replacing the first marble. Is this a discrete or continuous sample space? Two dice are thrown and the number of dots on each die is noted. Write the sample space in set notation. Let E be the event that the sum of the dice is odd. Describe E using set notation. Let F be the event that at least one of the dice lands on 1. Describe F using set notation. Let G be the event that the sum is 5. Describe G using set notation. Describe the events E F,E F,E Fc and E F G. A number x is selected at random in the interval [-1,1]. Let the events A = {x

Explanation / Answer

1.)

a.) Sample space S = {RR, GG, BB, RG, RB, GB, GR, BG ,BR}

b.) Sample space S = {RG, RB, GB, GR, BG ,BR}

c.) Discrete

2.)

a.) Sample space S = { (a,b)}   -1<a,b is an integer < 7 }

b.) E = { (a,b) |   a+b is odd, -1<a,b is an integer < 7 }

c.) F = { (1,b) , (a,1) |   -1 < a,b is an integer < 7 }

d.) G = { (a,b) |   a+b = 5 , -1<a,b is an integer < 7 }

e.) E intersection F = { (1,2) ,(1,4), (1,6), (2,1), (4,1), (6,1) }

E union F = { (a,b) , (1,1), (1,3), (1,5), (5,1), (3,1) |   a+b is odd, -1<a,b is an integer < 7 }

E union Fc = { (a,b) |   a+b is odd and (a,b) not equal to 1, -1<a,b is an integer < 7 }

E intersection F intersection G = { (1,4), (4,1) }

3.)

a.)

P(B) = 1-(-0.5) / 2 = 3/4 = 0.75

P(A intersection B) = 0.5 / 2 = 1/4 = 0.25

P(A intersection C) = 0.25 / 2 = 1/8 = 0.125

b.)

P(A union B) = 1

P(A union C) = (0.25+1) / 2 = 1.25/2 = 0.625

P(A union B union C) = 1

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.