# Calculating Probability Values

1. Compute the number of ways you can select n = 4 elements from N = II elements. There are _________ways to select 4 elements from 11 elements.

(Simpli fy your an swer.)

2. A magazine reported on an independent study of postal workers and violence at post offices. In a sample of 13,000 postal workers, 910 were physically assaulted on the job in a recent year. Use this information to estimate the probability that a randomly selected postal worker will be physically assaulted on the job during the year.

The probability that a randomly selected postal worker will be physically assaulted on the job during the year is ___. (Type an exact answer in simplified form.)

3. It was reported by an agency that, under its standard inspection system, two in every I00

slaughtered chickens pass inspection with fecal contamination.

If a slaughtered chicken is selected at random, what is the probability that it passes inspection with fecal contamination? The probability of part a was based on a study that found that 631 of 32,042 chicken carcasses passed inspection with fecal contamination. Do you agree with the agency's statement about the likelihood of a slaughtered chicken passing inspection with fecal contamination?

The probability is ___.(Type an integer or a decimal.)

Do you agree with the agency's statement?

Yes, because less than

No more than two in every I00 ch ickens in the sample of 32,042 were

Approximately

Exactly

contaminated.

4. From a list of 10 preferred stocks recommended by your broker , you will select three to invest in. How many different ways can you select the three stocks from the 10 recommended stocks?

There are ___ different ways to select the three stocks from the 10 recommended stocks.

5. Consider the following Venn diagram, where P(E 1) = P(E2) = P(E3) = ¼

4

P(E4) = P(E5) = ½ P(E6) = -1/10, and P(E7) = 1/20. Complete a through h .

a. Find P(A).

P(A) = ___ (Type an exact answer in simplified form.)

b. Find P(B).

P(B) = ___ (Type an exact answer in simplified form.)

c. Find P(AuB).

P(AuB) = ___ (Type an exact answer in simplified form.)

d. Find P(AnB).

P(AnB) = ___ (Type an exact answer in simplified form.)

e. Find P(A c).

P(A c)= ___(Type an exact answer in simplified form.)

P(B c) = ___ (Type an exact answer in simplified form.)

g. Find P(AuA c) .

P(AuA c)= ___ (Type an exact answer in simplified form .)

h. Find P(A cnB).

P(A cnB) = ___ (Type an exact answer in simplified form.)

6. The table represents the number of active-duty military personnel by rank in three major branches of the military. Complete parts a through g.

Army Navy Marines

Total

Officers 62,937 42,720 88,487 194,144

Enlisted 322,382 289,217 260,059 871,658

a. List the simple events for this experiment.

Let 0 represent an officer and E represent someone who is enlisted. Let A represent someone in the Anny, N represent someone in the Navy , and M represent someone in the Marines. Choose the correct answer below.

A. OA, ON, OM

B. AN, AM, OA, ON, OM

C. OA, ON, OM, EA, EN, EM

b. Assign reasonable probabilities to the simple events.

Select the correct choice below and fill in the answer boxes to complete your choice.

(Round to three decimal places as needed .)

A. P(OA) = P(ON) = P(OM) =

B. P(AN) = __,P(AM) = __,P(OA) = __,P(OA) = __,P(ON) = __,

P(OM) = ___

C. P(OA) = __,P(ON) = ___,P(OM) = ___,P(EA) = ____,

P(EN) = ___ ,P(EM) = ____

c. Find the probability that an active-duty military person is an officer. The probability is ___. (Round to three decimal places as needed.)

d. Find the probability that an active-duty military person is in the Navy. The probability is ___. (Round to three decimal places as needed.)

e. Find the probability that an active-duty military person is a Naval officer.

The probability is ____. (Round to three decimal places as needed .)

f. Find the probability that an active-duty military person is either an officer or is in the Navy .

The probability is ____. (Round to three decimal places as need ed.)

g. Find the probability that an active-duty military person is not in the Army.

The probability is ____. (Round to three decimal places as needed .)

7. The table to the right gives a breakdown of 2,126 civil cases that were appealed. The outcome of the appeal, as well as the type of trial (judge or jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal and type of trial are observed.

a. Find P(A), where A = {jury trial}.

P(A) = ___ (Round to three decimal places as needed.)

b. Find P(B), where B = {plaintiff trial win is reversed}. P(B) = ______ (Round to three decimal places as needed.)

c. Are A and B mutually exclusive events?

___ No

____ Yes

d. Find P(A c).

P(A c)= ___ (Round to three decimal places as needed.)

e. Find P(AuB).

P(AuB) = ___ (Round to three decimal places as needed.)

f. Find P(AnB).

P(AnB) = ___ (Round to three decimal places as needed

8. A table classifying a sampl e of 135

patrons of a restaurant according to type of

meal and their rating of the service is shown to the right. Suppose we select, at random , one of the 135 patron s. Given that the meal was dinner, what is the probability that the service was good?

Given that the meal was dinner, the probability that the service was good is __.

(Type an integer or a simplified fraction.)

9. In auditing a firm's financial statements, an auditor is required to assess the operationa l effectiveness of the accounting system. In performing the assessment, the auditor frequently relies on a random sample of actual transactions. A particular firm has 5,369 customer accounts that are numbered from 0001 to 5369.

a. One account is to be selected at random for audit. What is the probability that account

number 3,233 is selected?

___ (Round to six decimal places as needed.)

b. View the two possible random samples mentioned in the problem of size 10. Is one more likely to be selected than the other?

A. Yes, because a sample in num erical order has a much lower probability of occurring .

B. Yes, because the probability of selecting any particular sample of size 10 depends on the actual account numbers in the data set.

c. No, because the probability of selecting any particular sample of size I0 does not depend on the actual account numbers in the sample.

D. No, because 0008 occurs in the first sample and in the second sample.

Data Table

Sample Number 1

5025 5369 0963 0772 3448

2666 1123 0008 0026 4194

Sample Number 2

0001 0003 0005 0007 0009

0002 0004 0006 0008 0010

#### Solution Preview

1. Compute the number of ways you can select n = 4 elements from N = II elements. There are _________ways to select 4 elements from 11 elements.

(Simpli fy your an swer.)

In this selection, the order for the selected 4 elements are not important. Therefore, it is a problem of combination.

Based on the definition of combination, the total ways are: 11C4=11*10*9*8/(4*3*2*1)=330.

2. A magazine reported on an independent study of postal workers and violence at post offices. In a sample of 13,000 postal workers, 910 were physically assaulted on the job in a recent year. Use this information to estimate the probability that a randomly selected postal worker will be physically assaulted on the job during the year.

The probability that a randomly selected postal worker will be physically assaulted on the job during the year is ___. (Type an exact answer in simplified form.)

To calculate the probability, we need to use the formula: total number of postal worker being assaulted/total number of postal workers. In this case, probability=910/13000=7/100.

3. It was reported by an agency that, under its standard inspection system, two in every I00

slaughtered chickens pass inspection with fecal contamination.

If a slaughtered chicken is selected at random, what is the probability that it passes inspection with fecal contamination? The probability of part a was based on a study that found that 631 of 32,042 chicken carcasses passed inspection with fecal contamination. Do you agree with the agency's statement about the likelihood of a slaughtered chicken passing inspection with fecal contamination?

The probability is ___.(Type an integer or a decimal.)

Do you agree with the agency's statement?

Yes, because less than

No more than two in every I00 ch ickens in the sample of 32,042 were

Approximately

Exactly

contaminated.

Based on the question, it is known that two in 100 slaughtered chicken pass inspection with fecal ccontamination.

Therefore, probability that a randomly chosen chicken pass inspection with fecal contamination: 2/100=0.02

In the study, the probability is: 631/32042=0.0197.

Since 0.0197 is approximately two in every 100 chicken, we agree with the agency's statements.

4. From a list of 10 preferred stocks recommended by your broker , you will select three to invest in. How many different ways can you select the three stocks from the 10 recommended stocks?

There are ___ different ways to ...

#### Solution Summary

The probability values are calculated.