Question

1. the students who attend memorial high school have a wide variety of extra - curricular activities to choose from in the after - school program. students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. many students choose to participate in multiple activities. students have equal probabilities of being freshmen, sophomores, juniors, or seniors. if event a = sophomore or junior, what is event a?

• event a = junior or senior
• event a = sophomore or senior
• event a = freshman or junior
• event a = freshman or senior

Explanation:

Step1: Recall Complement Event

The complement of an event \( A \) (denoted \( A' \)) consists of all outcomes not in \( A \). Here, students are freshmen, sophomores, juniors, or seniors (4 mutually exclusive groups, equal probability). Event \( A \) is "sophomore or junior", so \( A' \) should be the students not in sophomore or junior.

Step2: Identify Non - A Groups

The groups not in "sophomore or junior" are freshmen and seniors. So \( A' \) is "freshman or senior".

Answer:

Event \( A' \) = freshman or senior (the fourth option: Event \( A' \) = freshman or senior)