MGT 201 Quantitative Analysis Winter 2018 Homework 3 Due Tuesday, January 30, 20

Question

MGT 201 Quantitative Analysis Winter 2018 Homework 3 Due Tuesday, January 30, 2018 1. You roll a pair of fair 6-sided dice: a red die and a blue die. (a) Consider event A: (the outcome of the red die is more than 3, and event B: (the outcome of the red die is less than 5). Given that event A occurs, what is the probability that event B occurs? (b) Are A and B mutually exclusive (i.e., disjoint)? (c) Are A and B independent? (d) Calculate the probability of event C: (the outcome of the red die is equal to the outcome of the blue die). (e) Consider event D: (the outcome of the red die is equal to 1). Calculate the probability of event C given that event D occurs (f) Are C and D independent? (g) Consider event E: fat least one die has an outcome equal to 2). Calculate the probability of event E given that event D occurs. 65% of Florida residents support raising the debt ceiling, ing the debt hat

Explanation / Answer

Event A: Outcome of red die is more than 3 => P(A) = 1/2; A_set = {4,5,6}

Event B: Outcome of red die is less than 5 => P(A) = 2/3; B_set = {1,2,3,4}

——

a)

P(B|A) = 1/3 [Answer (a)]

——

b)

NOT mutually exclusive => {4} exists as a mutual favourable condition [Answer (b)]

——

c)

P(A) = 1/2, P(B) = 2/3 => If they are independent, P(B|A) = P(B). But, P(B|A) = 1/3 (NOT equal to 2/3)

A and B are NOT independent [Answer (c)]

——

d)

Event C: Outcome of both die is equal => P(C) = 6/36; C_set = {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}

P(C) = 1/6 [Answer (d)]

——

e)

Event D: Outcome of red die is 1 => P(D) = 1/6; D_set = {1}

P(C|D) = 1/36; Favourable_set = {(1,1)} [Answer (e)]

——

f)

P(C|D) = P(C) = 1/6 and P(D|C) = P(D) = 1/6

C and D are independent [Answer (f)]

——

g)

Event E: Outcome of at least 1 die is 2 => P(E) = 11/36; E_set = {(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)}

For P(E|D) —> Possible_conditions_set = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} and favourable_set = {(1,2)}

P(E|D) = 1/6 [Answer (g)]

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

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