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Mrs. bergstedt teaches four classes. each class has 15 students. her first class has 9 juniors, her second class has 12 juniors, her third class has 6 juniors, and her fourth class has 3 juniors. if she randomly chooses one student from each class to complete a problem on the board, what is the probability that she selects four students that are not juniors?

Respuesta :

sharmaenderp
To find the probability of selecting four students that are not juniors, we must find the number of students who are not juniors in each class. So, we have

First class = 15 - 9 = 6
Second class = 15 - 12 = 3
Third class = 15 - 6 = 9
Fourth class = 15 - 3 = 12

Thus, for each class, we can get the probability that the selected student is not a junior as shown below.

First class = 6/15
Second class = 3/15
Third class = 9/15
Fourth class = 12/15

To find the probability of selecting four students that are not juniors, we multiply the probabilities from the four classes.

[tex] P = (\frac{6}{15})(\frac{3}{15})(\frac{9}{15})(\frac{12}{15}) [/tex]
[tex] P = \frac{6(3)(9)(12)}{15^{4}} [/tex]
[tex] P = 0.0384 [/tex]

Thus, Mrs Bergstedt has a probability of 0.0384 of selecting four students that are not juniors.

Answer: 0.0384

Answer: 0.0.256

In each case we have 15^4 as the denominator

and the sum of the numerators is

9 *3*9*12 + (first only)

6* 12 *9*12 + (second only)

6*3* 6 *12 + (third only)

6*3*9* 3 (fourth only)


Each number has a 3 as a factor, which can cancel a 3 in the one of the 15's

Now we have

3*1*3*4 +

2*4*3*4 +

2*1*2*4 +

2*1*3*1 all over 5^4

so finally

(36+96+16+6) / 5^4 = 0.2464

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