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?

Question

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?

Answer 1

Number(AorBorC)= Number(A) + Number(B) + Number(C) - Number(AandB) - Number(AandC) - Number (BandC) + Number(AandBandC)

= 94 + 86 + 95 - 37 - 43 - 42 + 8
= 161

Prob of (as stated) = 8/161

You could also find the total by using Venn diagrams

Answer 2

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 in the school.

First, let's count the number of students taking all three courses. We are given that 28 students take all three subjects (biology, ethnic studies, and geometry).

To get the total number of students in the school, we need to count the number of students taking each subject and subtract the overlaps.

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 = 37
Number of students taking both geometry and ethnic studies = 43
Number of students taking both ethnic studies and biology = 42

To calculate the total number of students, we can use the principle of inclusion-exclusion:

Total = B + E + G - (students taking both B and G) - (students taking both G and E) - (students taking both E and B) + (students taking all three subjects)

Total = 94 + 86 + 95 - 37 - 43 - 42 + 28
Total = 261

Now we can calculate the probability:

Probability of a student taking all three courses = (Number of students taking all three courses) / (Total number of students)

Probability of a student taking all three courses = 28 / 261 ≈ 0.1075

Therefore, the probability that a student chosen at random will be taking all three courses is approximately 0.1075 or 10.75%.