Question

does choosing a blue marble represent the complement event of choosing a red marble? explain.
image of marbles: b (cyan), b (cyan), r (red), p (purple), p (purple)
choosing the blue marble i dont think it represents the complement of event of choosing the red one but i think its just when possible outcome inside of choosing the red but not necessarily the entire complement.
sample response: the complementary event for choosing a red marble is choosing a blue or purple. the total number of marbles is 5. the probability of choosing a red marble is 1/5, and the complement
complementary events must have a sum of 1. which of the following did you include in your response? check all that apply.
☐ no, the probability of choosing a red marble is not the complement of choosing a blue marble.
☐ p(red) + p(blue) = 3/5, not 1.
☐ the number of blue and red marbles does not add to the total number of outcomes.
☐ there are other marbles besides red ones and blue ones.

Explanation:

To determine the correct options, we analyze each:

1. "No, the probability of choosing a red marble is not the complement of choosing a blue marble."

Complementary events have probabilities that sum to 1. Since there are purple marbles too, \( P(\text{red}) + P(\text{blue})
eq 1 \), so this is correct.

1. "\( P(\text{red}) + P(\text{blue}) = \frac{3}{5} \), not 1."

Count marbles: 2 blue (B), 1 red (R), 2 purple (P) → total = 5.
\( P(\text{red}) = \frac{1}{5} \), \( P(\text{blue}) = \frac{2}{5} \). Sum: \( \frac{1}{5} + \frac{2}{5} = \frac{3}{5}
eq 1 \). Correct.

1. "The number of blue and red marbles does not add to the total number of outcomes."

Blue (2) + red (1) = 3, total outcomes = 5. 3 ≠ 5. Correct.

1. "There are other marbles besides red ones and blue ones."

There are purple marbles, so this is true. Correct.

Answer:

A. No, the probability of choosing a red marble is not the complement of choosing a blue marble.
B. \( P(\text{red}) + P(\text{blue}) = \frac{3}{5} \), not 1.
C. The number of blue and red marbles does not add to the total number of outcomes.
D. There are other marbles besides red ones and blue ones.