Step 1 :

13).

Total test subjects are 1000.

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

randomly select 2 subjects and get 2 results that are both false positive results.

Step 2 :

a).

Find the probability that they both false positive results.

Assume that the 2 selections are made with replacement.

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.

Assume that the 2 selections are made with replacement.

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 0.00801 .

Step 1)

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 True positive result is 44.

The total number of True negative result is 860.

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

(a)

Find the probability of selecting correct results with replacement.

Assume that the 3 selections are made with replacement.

Let the three subjects are .

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.

Step 2:

(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 true results from the three subjects is

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

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.

Step 1:

(17)

Number of  heart pacemaker are 8834.

Number of malfunction caused by firmware are 504.

The number of  good heart pacemaker are 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 the entire batch will be accepted is 0.9986.

Solution:

The probability the entire batch will be accepted is 0.9986.