Question

a bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
which best describes the complement of choosing a red marble?
choosing a blue, green, or yellow marble
choosing any marble
choosing a green or blue marble
choosing a yellow marble

Explanation:

Step1: <Understand the concept of complementary events>

The complement of an event \(A\) is all the outcomes that are not in \(A\). The sum of the probability of an event and its complement is \(1\).

Step2: <Count the total number of marbles>

The total number of marbles \(n = 1+2 + 3+3=9\).

Step3: <Count the number of non - red marbles>

The number of non - red marbles (blue, green, yellow) is \(1 + 2+3=6\).

Step4: <Analyze each option>

• Option "choosing a blue, green, or yellow marble":

The number of blue, green, or yellow marbles is \(1 + 2+3 = 6\). The complement of choosing a red marble is choosing a non - red marble (blue, green, or yellow).

• Option "choosing any marble": This is the sample space and not the complement.
• Option "choosing a green or blue marble": The number of green or blue marbles is \(2 + 1=3

eq6\).

• Option "choosing a yellow marble": The number of yellow marbles is \(3

eq6\).

Answer:

choosing a blue, green, or yellow marble