Question

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?

Answer 1

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.

$P = (\frac{6}{15})(\frac{3}{15})(\frac{9}{15})(\frac{12}{15})$
$P = \frac{6(3)(9)(12)}{15^{4}}$
$P = 0.0384$

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

Answer: 0.0384

Answer 2

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