At rosemead high school, 94 students take biology, 86 take ethnic studies, and 95 take geometry. thirty-seven students take both biology and geometry, 43 take geometry and ethnic studies, and 42 take ethnic studies and biology. twenty eight students take all three subjects. What is the probability that a student chosen at random will be taking all three of the courses?

28/total number of students

To find the probability that a student chosen at random will be taking all three courses, we need to divide the number of students taking all three courses by the total number of students.

First, let's gather the information we need:

- Number of students taking biology (B): 94
- Number of students taking ethnic studies (E): 86
- Number of students taking geometry (G): 95
- Number of students taking both biology and geometry (B ∩ G): 37
- Number of students taking both geometry and ethnic studies (G ∩ E): 43
- Number of students taking both ethnic studies and biology (E ∩ B): 42
- Number of students taking all three courses (B ∩ E ∩ G): 28

To find the total number of students, we need to add the number of students taking each subject individually:

Total number of students = B + E + G

To avoid double-counting, we need to subtract the number of students taking each pair of subjects:

Total number of students = B + E + G - (B ∩ G) - (G ∩ E) - (E ∩ B)

Plugging in the given information:

Total number of students = 94 + 86 + 95 - 37 - 43 - 42

Now we can find the probability by dividing the number of students taking all three courses by the total number of students:

Probability = (B ∩ E ∩ G) / (Total number of students)

Plugging in the values:

Probability = 28 / (94 + 86 + 95 - 37 - 43 - 42)

After calculating the total number of students, we can divide 28 by that number to find the probability.