does choosing a blue marble represent the complement event of choosing a red marble? explain.
does choosing a blue marble represent the complement event of choosing a red marble? explain.
Answer
Explanation:
Step1: Define complement event
The complement of an event A is all outcomes that are not in A. For two - events to be complements, they must be mutually exclusive (no overlap) and their union must be the entire sample space.
Step2: Analyze the sample space
The sample space here is {B, B, R, P, P} where B is blue, R is red and P is purple.
Step3: Check mutual - exclusivity and union
The events of choosing a blue marble and choosing a red marble are mutually exclusive since a marble can't be both blue and red at the same time. However, their union is not the entire sample space because there are also purple marbles. So they are not complements.
Answer:
No, because the union of choosing a blue marble and choosing a red marble does not equal the entire sample space (there are purple marbles in the sample space).