Question

A guidance counselor is planning schedules for 30 students. 16 want to take Spanish and 11 want to take Latin. 5 say they want to take both. What is the probability that the student studies neither subject?

Answer 1

The probability that a student studies neither Spanish nor Latin is 8/30 or approximately 0.267, calculated by subtracting the number of students taking at least one language from the total number of students.

Step-by-step explanation:

To calculate the probability that a student studies neither Spanish nor Latin, we use the principle of inclusion-exclusion. We first add the number of students wanting to take Spanish and Latin: 16 (Spanish) + 11 (Latin) = 27 students.

However, this counts the 5 students who want to take both languages twice. To adjust, we subtract those 5 students once: 27 - 5 = 22 students taking at least one language.

Now, we subtract the 22 students taking at least one language from the total number of students to find those taking neither language: 30 (total students) - 22 (at least one language) = 8 students taking neither.

The probability that a student studies neither subject is the number of students studying neither divided by the total number of students. Therefore, the probability is 8/30 or approximately 0.267 (or 26.7%).