6. A bag contains 9 marbles. Three marbles are red, two are green, and the others are blue. What is the probability that a blue or green marble will be chosen? Give your answer as a ratio.

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UpStudy AI · Accepted Answer

**Step 1:**  
The bag contains a total of $$9$$ marbles.

**Step 2:**  
There are $$3$$ red marbles and $$2$$ green marbles. The rest are blue, so the number of blue marbles is:  
$$
9 - (3+2) = 4.
$$

**Step 3:**  
The probability of choosing a blue or green marble involves $$4$$ blue and $$2$$ green marbles, totaling:  
$$
4 + 2 = 6 \text{ favorable outcomes}.
$$

**Step 4:**  
The probability is given by the ratio of favorable outcomes to the total outcomes:  
$$
\frac{6}{9}.
$$

**Step 5:**  
Simplify the fraction by dividing the numerator and denominator by $$3$$:  
$$
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}.
$$

The probability, expressed as a ratio, is $$\mathbf{2:3}$$.
The probability of choosing a blue or green marble is $$2:3$$.

A bag contains 9 marbles. Three marbles
are red, two are green, and the others are
blue. What is the probability that a blue
or green marble will be chosen? Give
your answer as a ratio.

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