Question

does choosing a blue marble represent the complement event of choosing a red marble? explain.

Explanation:

Step1: Recall Complement Event Definition

A complement event of an event \( A \) (choosing red) is the set of all outcomes not in \( A \). So, complement of choosing red should be choosing non - red marbles.

Step2: Analyze Marbles' Colors

Marbles: 2 blue (B), 1 red (R), 2 purple (P). Non - red marbles are blue + purple (\(2 + 2=4\) marbles), while blue marbles are 2. Since complement of red should include all non - red (blue and purple), blue alone is not all non - red.

Answer:

No. The complement of choosing a red marble should be choosing a non - red marble. The non - red marbles include blue and purple marbles (since there are blue, red, and purple marbles). Choosing a blue marble is only part of the non - red marbles (not all non - red marbles, as purple marbles are also non - red), so choosing a blue marble is not the complement event of choosing a red marble.