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Chapter 3: 3 (page 168)

The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:

a. Either 1,2 or 3 occurs

b. Either 1,3 or 5 occurs

c. 4 does not occur

Short Answer

Expert verified

a.PA=0.55,b.PB=0.50,c.P(C)=0.70

Step by step solution

01

Finding the probability of event  A

To calculate the probability of event A happening, we add the individual probabilities of sample points 1, 2 and 3.

Given,

A: Either 1,2 or 3 occurs

P(A)=P(1)+P(2)+P(3)P(A)=0.05+0.20+0.30P(A)=0.55PA=P1+P2+P3PA=0.05+0.20+0.30PA=0.55

Hence, P(A)=0.55PA=0.55

02

Finding the probability of event  B

To calculate the probability of event B happening, we add the individual probabilities of sample points 1, 3 and 5.

B: Either 1,3 or 5 occurs

P(B)=P(1)+P(3)+P(5)P(B)=0.05+0.30+0.15P(B)=0.50PB=P1+P3+P5PB=0.05+0.30+0.15PB=0.50

Hence, P(B)=0.50PB=0.50

03

Finding the probability of event C

To calculate the probability of event C happening, we subtract the probability of sample point 4 occurring from 1.

C: 4 does not occur

P(C)=1-P(C)P(C)=1-0.30P(C)=0.70PC=1-PCPC=1-0.30PC=0.70

Hence,P(C)=0.70PC=0.70

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Most popular questions from this chapter

Firefighter glove sizing. Human Factors (December 2015) published a study on how well firefighter gloves fit. In a group of 586 firefighters who reported their glove size, the researchers determined whether the gloves fit well or poorly by gender. The data are summarized in the accompanying table. Consider the gender and glove fit status of a randomly selected firefighter.

a. List the sample points for this experiment.

b. Assign reasonable probabilities to these sample points.

c. Find the probability the firefighter is a female.

d. Find the probability the glove fits well.

e. Find the probability the firefighter is a female and has a well-fitting glove.

f. Find the probability the firefighter is a female or has a well-fitting glove.

Glove Fits Well

Glove Fits Poorly

Totals

Males

415

132

547

Females

19

50

39

Totals

434

152

586

Source: H. Hsiao, et al., 鈥淔irefighter Hand Anthropometry and Structural Glove Sizing: A New Perspective,鈥� Human Factors, Vol. 57, No. 8, December 2015 (Table 6).

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 accompanying two-way table gives the probabilities associated with each of the six possible outcome pairs.

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. FindP(AC).

f. FindP(A鈭�B).

g. FindP(A鈭�B).

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.

Management system failures. Refer to the Process Safety Progress (December 2004) study of 83 industrial accidents caused by management system failures, Exercise 2.150(p. 142). A summary of the root causes of these 83 incidents is reproduced in the following table. One of the 83 incidents is randomly selected and the root cause is determined.

Management system cause category

Number of incidents

Engineering and design

27

Procedures and practices

24

Management and oversight

22

Training and communication

10

Total

83

a. List the sample points for this problem and assign reasonable probabilities to them.

b. Find and interpret the probability that an industrial accident is caused by faulty engineering and design.

c. Find and interpret the probability that an industrial accident is caused by something other than faulty procedures and practices.

For two events, A and B, P(A)= .4, P(B)= .2 , and P(A鈭�B) = .1:

a. Find P (A/B).

b. Find P(B/A).

c. Are A and B independent events?

Patient medical instruction sheets. Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects. One method of increasing patients鈥� awareness of the problem is for physicians to provide patient medication instruction (PMI) sheets. The American Medical Association, however, has found that only 20% of the doctors who prescribe drugs frequently distribute PMI sheets to their patients. Assume that 20% of all patients receive the PMI sheet with their prescriptions and that 12% receive the PMI sheet and are hospitalized because of a drug-related problem. What is the probability that a person will be hospitalized for a drug-related problem given that the person received the PMI sheet?
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