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.

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 would be 4/5. That is not the same as choosing a blue marble.

choosing a blue marble does not represent the complement event of choosing a red marble because 2/5 ≠ 4/5.

Step-by-step explanation:

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

The total number of marbles ⇒ 2 blue + 1 red + 2 purple = 5 marbles.

To find the probability of choosing a blue marble:

P (blue) = No. of blue marbles / Total marbles

⇒ 2 / 5

To find the complement event of choosing a red marble:

Complement of an Event is defined as all the outcomes that are NOT the event. So the Complement of an event is all the other outcomes (not the ones we want).

Complement of choosing red ⇒ P (not getting red marble)

P (not getting red marble) = No. of marbles other than red / Total marbles

⇒ 4 / 5

Therefore, P (blue) is not equal to P (not getting a red).

⇒ 2/5 ≠ 4/5

So, choosing a blue marble does not represent the complement event of choosing a red marble.