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[answered] 1a)Suppose that 11% of a certain batch of calculators have


1a)Suppose that 11% of a certain batch of calculators have a defective case, and that 12% have defective batteries. Also, 5% have both a defective case and defective batteries. A calculator is selected from the batch at random. Find the probability that the calculator has a good case and good batteries.

The probability that the calculator has a good case and good batteries is?


1b)The following table gives a future year's projected civilian labor force probability distribution by age and gender.

Age

Male

Female

Total

16-24

0.068

0.062

0.130

25-54

0.345

????0.293

??????????0.638

55 and over

0.122

0.110

0.232

Total

0.535

0.465

1.00

Find the probability that a randomly selected worker is the following.

a. Female and 16 to 24 years old

c. Male or 25 to 54 years old

b.?16 to 54 years old

d.?Female or 16 to 24 years old


1c) The probability that a visit to a primary care physician's (PCP) office results in neither lab work nor referral to a specialist is 28%. Of those coming to a PCP's office, 25% are referred to specialists and 51%

require lab work. Determine the probability that a visit to a PCP's office results in both lab work and referral to a specialist. What is the probability that a visit results in both lab work and referral to a specialist?


2a)The following data were gathered for 120 workers. Of those workers, 49 were women,

2 women earned more than $40,000, and 56 men earned $40,000 or less. Complete parts a through d below.

a.?Find the probability that an individual is a woman earning $40,000 or less.

b.?Find the probability that an individual is a man earning more than $40,000.

c.?Find the probability that an individual is a man or is earning more than $40,000.

d.?Find the probability that an individual is a woman or is earning $40,000 or less.

3a)The management of a firm wishes to check on the opinions of its assembly line workers. Before the workers are interviewed, they are divided into various categories. Define events E, F, and G as shown below. Complete parts a through f.

E: worker is male

F: worker has worked more than 6 years

G: worker does not contribute to a voluntary retirement plan

Describe the event E???F in words?

Describe the event E???G??in words.

Describe the event F??in words.

Describe the event F???G in words.

Describe the event F????G??in words.


3b)For a medical experiment, people are classified as to whether they smoke,

have a family history of diabetes or are shorter than average

Define events E, F, and G, as shown below. Complete parts a through c.

E: person smokes

F: person has a family history of diabetes

G: person is shorter than average

Describe the event G??in words

Describe the event F???G in words

Describe the event E???G??in words.


3c)Several friends chartered a boat for a day's fishing. They caught a total of 52

fish. The table below provides information about the type and number of fish caught. Determine the empirical probability that the next fish caught is a grouper

Fish

Number caught

Grouper

11

Shark

13

Flounder

4

Kingfish

24

1a) The given table indicates the transactions for one teller for one day. Letting ?E 1?represent "cashing a check" and E2?represent "making a deposit," express P(E1'|E2') in words and find its value.

Transaction

Cash Check

No Check

Totals

Make Deposit

12

15

27

No Deposit

18

14

32

Totals

30

29

59


1b)Among uses of automated teller machines (ATMs),92% use ATMs to withdraw cash and 32% use them to check their account balance. Suppose that 97% use ATMs to either withdraw cash or check their account balance (or both). Given a woman who uses an ATM to check her account balance, what the probability that she also uses an ATM to get cash?

The probability is?

1c) A bicycle factory runs two assembly lines, A and B. 97% of line A's products pass inspection and 95%

of line B's products pass inspection. 50% of the factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the factory's bikes passed inspection and came off assembly line A The probability is?

2a)In 2002, 66.1% of men and 50.2% of women in a country were overweight. Given that 48.2%

of adults are men and 51.8% Are women, find the probability that a randomly selected adult fits the following description.

a.?Probability An overweight man?

B.probability an Overweight adult?

c.?Are the events that an adult is a man and that an adult is overweight independent? Explain.


2b)The table shows the results of a restaurant survey. Find the probability

P(X|D).

Meal

Service Great(A)

Service Good(B)

Service Okay(C)

Service Poor(D)

Total

Lunch (X)

36

17

11

29

93


Dinner (Y)

18

38

43

49

148


Total

54

55

54

78

241



3a) A teacher has found that the probability that a student studies for a test is 0.72, and the probability that a student gets a good grade on a test is 0.88, and the probability that both occur is 0.71.

a.?Are these events independent?

b.?Given that a student studies, find the probability that the student gets a good grade.

c.?Given that a student gets a good grade, find the probability that the student studied.


3b)A manufacturing firm finds that 40% of its new hires turn out to be good workers and 60%

become poor workers. All current workers are given a reasoning test. Of the good workers,60%

pass it; 30% of the poor workers pass it. Assume that these figures will hold true in the future. If the company makes the test part of its hiring procedure and only hires people who meet the previous requirements and also pass the test, what percent of the new hires will turn out to be good workers?


3c)Of all the people applying for a certain job,70% are qualified and 30% are not. The personnel manager claims that she approves qualified people 85% of the time; she approves unqualified people 10% of the time. Find the probability that a person is qualified if he or she was approved by the manager. ?The probability is ?


1.

 

1a)

 

p(good case and good batteries) = 1 ? p(bad case or bad battery)

 

p(bad case or bad battery) = p(bad case) + p(bad battery) ?p(bad case and bad battery)

 

p(bad case or bad battery) = 0.11...

 


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