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There are 82 seniors at your school and three AP courses offered: AP Statistics, AP Calculus, and AP Biology.

- 30 students take AP Statistics.
- 26 students take AP Calculus.
- 25 students take AP Biology.
- 5 students take all three courses.
- 6 students take both AP Calculus and AP Biology.
- 10 students only take Biology.

If you select a senior at random, what is the probability that they take AP Statistics and AP Biology, but not AP Calculus?

Answer :

Final answer:

The probability that a randomly selected senior takes AP Statistics and AP Biology, but not AP Calculus, is 24 out of 82. This is found by subtracting students taking all three subjects and those taking AP Calculus and AP Biology, but not AP Statistics, from the total number of students taking AP Statistics.

Explanation:

To calculate the probability that a randomly selected senior takes AP Statistics and AP Biology, but not AP Calculus, we need to consider the given numbers and apply the principle of set subtraction in probability. First, let's identify the known values:

  • Total number of students taking AP Statistics: 30
  • Total number of students taking AP Calculus: 26
  • Total number of students taking AP Biology: 25
  • Number of students taking all three AP courses: 5
  • Number of students taking both AP Calculus and AP Biology: 6
  • Number of students only taking AP Biology: 10
  • Total number of seniors: 82

Since 5 students are taking all three courses, these are included in the counts for statistics and biology already. Out of the 6 students taking both calculus and biology, 5 are also in the all three category, leaving 1 student who takes both but not statistics.

We also know there are 10 students who take only biology. So, to find the number of students taking statistics and biology but not calculus, we'd take the total number taking statistics (30) and subtract those who take calculus (all three and the extra one), and also subtract the 10 that only take biology.

Calculation:

Total taking AP Statistics and AP Biology = 30 (AP Statistics) - 5 (all three AP courses) - 1 (AP Calculus and AP Biology without statistics) = 24

The probability is then:

Probability = Number of students taking AP Statistics and AP Biology but not AP Calculus / Total number of seniors

Probability = 24 / 82

Therefore, the probability is 24/82, which can be simplified if preferred.

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