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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich
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The outcomes of two variables are (Low, Medium, High) and

Chapter 3, Problem 33E

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QUESTION:

Problem 33E

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.

Low

Medium

High

On

.50

.10

.05

Off

.25

.07

.03

Consider the following events:

A: {On}

B: {Medium or On}

C: {Off and Low}

D: {High}

a. Find P(A).

b. Find P(B).

c. Find P(C).

d. Find P(D).

e. Find P(Ac).

f. Find P(A ∪ B).

g. Find P(A ∩ C).

h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.

Questions & Answers

QUESTION:

Problem 33E

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.

Low

Medium

High

On

.50

.10

.05

Off

.25

.07

.03

Consider the following events:

A: {On}

B: {Medium or On}

C: {Off and Low}

D: {High}

a. Find P(A).

b. Find P(B).

c. Find P(C).

d. Find P(D).

e. Find P(Ac).

f. Find P(A ∪ B).

g. Find P(A ∩ C).

h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.

ANSWER:

Solution:

Step 1 of 9:

We have the probabilities of Low, Medium, and High.

Low

Medium

High

On

0.50

0.10

0.05

Off

0.25

0.07

0.03

Then, A ={On}

          B = {Medium or On}

          C = {Off or Low}

         D = {High}

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