h4lp with stats homework The outcomes of two variables are L

h4lp with stats homework

The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table. Consider the events below. Complete parts a through h. On Off 0.48 0.26 Medium0.1 0.05 0.06 0.04 Hi B: {High or On] D: {Medium] A: {High} C: {Off and Low a. Find P(A) P(A)(Type an exact answer in simplified form.) b. Find P(B) PB)- (Type an exact answer in simplified form.) c. Find P(C) P(C)(Type an exact answer in simplified form.) d. Find P(D) P(D)- (Type an exact answer in simplified form.) e. Find P(A) P(A)- (Type an exact answer in simplified form.) f. Find P(AUB) P(C)-CType an exact ans

Solution

a)

P(A) = 0.06 + 0.04 = 0.10

b)

P(B) = 0.48+0.11+0.06+0.04 = 0.69

c)

P(C) = 0.26+0.05+0.04+0.48 = 0.83

d)

P(D) = 0.11+0.05 = 0.16

e)

P(Ac) = 1 - P(A) = 0.90

f)

As A is a subset of B,

P(A U B) = P(B) = 0.69

g)

high and low can\'t be together, so,

P(A n C) = 0

h)

Low, medium, and high can\'t go together.

On and off can\'t go together.

Thus, these are mutually exclusive:

A and C, A and D, B and C, C and D. [OPTION B]