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Question

(a) determine whether events A and B are independent or dependent, and (b) find P (A and B), the probability

9. A When one of the 222 coins listed in Data Set 21 is randomly selected, it is one of the 5 Indian pennies.

B: When one of the 222 coins listed in Data Set 21 is randomly selected, it is also one of the 5 Indian pennies

 

Indian Pennies

3.0630

3.0487

2.9149

3.1358

2.9753

 

11 A: When a survey subject is randomly selected from the 100 senators in the 111^th Congress, it is one of 58 Democrats.

B: When a second different senator is randomly selected, it is the one senator who is Independent.

Use the chart below to answer 13 and 15

	Positive Test Result (Drug Use Is Indicated)	Negative Test Result (Drug Use Is Not Indicated
Subject Uses Drugs	44 (True Positive)	6 (False Negative)
Subject Is Not a Drug User	90 (False Positive)	860 (True Negative)

 

13. If 2 of the 1000 test subjects are randomly selected, find the probability that they both false positive results. Is it unlikely to randomly select 2 subjects and get 2 results that are both false positive results?

 

a. Assume that the 2 selections are made with replacement.

a. Assume that the 2 selections are made without replacement

 

15. If 3 of the 1000 test subjects are randomly selected, find the probability that they all have correct test results (either true positive or true negative). Is such an event unlikely?

a. Assume that the 3 selections are made with replacement.

a. Assume that the 3 selections are made without replacement

 

17. Acceptance Sample, a sample of items is randomly selected without replacement and accepted if every item in the entire batch is okay. Among the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware. If the firmware is tested in three different pacemaker randomly selected from this back of 8834, what is the probability that the firmware in the entire batch will be accepted? Does this procedure suggest that the entire batch consists of good pacemakers? Why or why not?

 

Comments

11).

Please provide the table concerning the 100 senators in the 111^th Congress.

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9)

Please provide us the complete data.

 

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they don't prove the chart concering the 100 senators

Answer 1

Step 1 :

13).

Total test subjects are 1000.

Out of 1000 test subjects 2 test subjects are selected randomly.

The results obtained from 2 subjects are both false positive results.

Step 2 :

a).

Assume that the 2 selections are made with replacement.

 

Find the probability that they both false positive results.

Let the two subjects are .

From the table false positive results are 90.

Probability of selecting subject : .

Probability of selecting subject : .

The probability that they both false positive results, that the 2 selections are made with replacement : .

Thus, the probability is 0.0081 .

Step 3 :

b).

Assume that the 2 selections are made without replacement.

Find the probability that they both false positive results.

From the table false positive results are 90.

Probability of selecting subject : .

Probability of selecting subject : .

The probability that they both false positive results, that the 2 selections are made with out replacement : .

Thus, the probability is 0.00801 .

Solution :

a). The probability that they both false positive results, that the 2 selections are made with replacement is 0.0081 .

b). The probability that they both false positive results, that the 2 selections are made with out replacement is 0.00801.

Answer 2

Step 1:

(15)

The total number of subjects are 1000.

Out of 1000 test subjects 3 test subjects are selected randomly.

The results obtained from 3 subjects are correct results.

The total number of correct positive result is 44.

The total number of correct negative result is 860.

Total number of correct results(both positive and negative) are 44+860 = 904.

Step 2:

(a)

Find the probability of selecting correct results with replacement.

Assume that the 3 selections are made with replacement.

Let the three subjects be .

Probability of selecting subject  is .

Probability of selecting subject  is .

Probability of selecting subject is .

The three events are independent events then .

Probability of selecting correct results from the three subjects is

Probability of selecting correct results from the three subjects with replacement is 0.7387.

Comments

Contd..

Step 3:

(b)

Assume that the 3 selections are made without replacement.

Probability of selecting subject  is .

Now total number of subjects left are 999.

Number of correct results are 903.

Probability of selecting subject is .

Now total number of subjects left are 998.

Number of correct results are 902.

Probability of selecting subject is .

The three events are independent events then .

Probability of selecting correct results from the three subjects is

Probability of selecting correct results from the three subjects without replacement is 0.7385.

Since both the values of probability are almost equal, we can say that the events are equally likely.

Solution:

(a) Probability of selecting correct results from the three subjects with replacement is 0.7387.

(b) Probability of selecting correct results from the three subjects without replacement is 0.7385.

The events are equally likely.

Answer 3

Step 1:

(17)

Number of heart pacemaker is 8834.

Number of malfunction caused by firmware is 504.

The number of good heart pacemaker is 8834-504 = 8330.

The firmware is tested in three different pacemaker.

Find the probability the entire batch will be accepted without replacement.

Let the three units be .

Probability of good first unit of heart pacemaker is .

Probability of good second unit of heart pacemaker (without replacement) is .

Probability of good third unit of heart pacemaker (without replacement) is .

The three events are independent events then .

The probability the entire batch will be accepted is

The probability that the entire batch will be accepted is 0.9986.

Solution:

The probability that the entire batch will be accepted is 0.9986.