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ahrayia [7]
3 years ago
13

The probability that all four test subjects had a true negative test result when they are randomly selected without replacement

is nothing
Mathematics
1 answer:
algol133 years ago
6 0

The solution would be like this for this specific problem:

Given:

                                                                                                                No (Did Not Lie)                Yes (Lied)

Positive Test Result                                                                                         10                           29

(Positive test indicated that the subject lied.)                      (false positive)                  (true positive)

Negative test result                                                                                         66                           18

(Polygraph test indicated that the subject did not lie.)     (true negative)                  (false negative)

 

Find:


The probability that all four test subjects had a true negative test result when they are randomly selected without replacement.

Formula:

(66/123) x (65/122) x (64/121) x (63/120) = 0.0793864272

 

Therefore, when they are randomly selected without replacement, the <span>probability that all four test subjects had a true negative test result is 0.079</span>.

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First, let's write what we know.

We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.

Then, taking the third line, we can write an inequality:

C < L < G

C < 7 < C + 4

C - 4 < 3 < C

3 < C < 7

If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.

Then, we need to find how many students are in the play.

C + L + G

C + 7 + C + 4

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So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.

0.3T = 2C + 11

(Divide by 3/10 or multiply by 10/3 on both sides)

T = 20/3 C + 110/3

We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.

T = 20/3 * 4 + 110/3

T = 190/3

T = 20/3 * 5 + 110/3

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We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class.  We now need to figure out the number of student in her class.

The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.

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