Question

Does choosing a blue marble represent the complement event of choosing a red marble? Explain.

2 blue marbles, 1 red marble, and 2 purple marbles.

Answer 1

No.

The complement of "choose a red marble" is "choose a marble that is not red" — i.e., choose blue OR purple. Here there are 5 marbles total (2 blue, 1 red, 2 purple), so
- P(red) = 1/5
- P(blue) = 2/5
- P(not red) = P(blue or purple) = 4/5 = 1 − P(red).

Choosing blue (2/5) is only part of the complement (4/5), so it is not the complement unless blue were the only non-red color.