Question

let the universal set, u, be the set of students at central high, a be the set of students taking algebra, and c be the set of students taking chemistry. if a student is selected at random, describe in words what is meant by each of the following probabilities.
a. ( p(a cup c) )
b. ( p(a cap c) )
c. ( 1 - p(c) )

a. the probability of a student not taking algebra
b. the probability of a student taking algebra or chemistry
c. the probability of a student not taking chemistry
d. the probability of a student taking algebra and chemistry

c. describe the meaning of the probability ( 1 - p(c) ) in words. choose the correct answer below.
a. the probability of a student taking chemistry
b. the probability of a student not taking algebra
c. the probability of a student taking algebra
d. the probability of a student not taking chemistry

Explanation:

For part c, we know that \( P(C) \) is the probability of a student taking chemistry. By the complement rule in probability, \( 1 - P(C) \) represents the probability of the complement event of \( C \), which is a student not taking chemistry. Now let's analyze the options:

• Option A: \( P(C) \) is the probability of taking chemistry, not \( 1 - P(C) \), so A is wrong.
• Option B: The probability of not taking algebra would be \( 1 - P(A) \), not related to \( 1 - P(C) \), so B is wrong.
• Option C: \( P(A) \) is the probability of taking algebra, not \( 1 - P(C) \), so C is wrong.
• Option D: Matches the interpretation of \( 1 - P(C) \) as the probability of not taking chemistry.

Answer:

D. The probability of a student not taking chemistry