A bag contains 3 blue marbles, 3 red marbles, and 4 yellow marbles. The probability of drawing a blue marble out of the
bag is or . How many of what color of marbles must be added to the bag so that the probability of a blue marble
being drawn at random from the bag is ?
Select the correct answer below and fill in the answer box within your choice.
(Type a whole number.)
A. There must be red marbles added to the bag.
B. There must be 18 blue marbles added to the bag.
C. There must be yellow marbles added to the bag.

Ask by Owen Kirk. in the United States

Jan 24,2025

Question

A bag contains 3 blue marbles, 3 red marbles, and 4 yellow marbles. The probability of drawing a blue marble out of the
bag is or . How many of what color of marbles must be added to the bag so that the probability of a blue marble
being drawn at random from the bag is ?
Select the correct answer below and fill in the answer box within your choice.
(Type a whole number.)
A. There must be red marbles added to the bag.
B. There must be 18 blue marbles added to the bag.
C. There must be yellow marbles added to the bag.

Ask by Owen Kirk. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To achieve a $$ 75\% $$ probability of drawing a blue marble from the bag, we need to determine how many additional blue marbles must be added.

**Initial Setup:**
- Blue marbles: 3
- Red marbles: 3
- Yellow marbles: 4
- **Total marbles initially:** $$ 3 + 3 + 4 = 10 $$

**Desired Probability:**
$$ \frac{\text{Number of Blue Marbles}}{\text{Total Number of Marbles}} = 75\% = \frac{3}{4} $$

Let $$ x $$ be the number of blue marbles to add. The new total number of marbles will be $$ 10 + x $$, and the new number of blue marbles will be $$ 3 + x $$.

Set up the equation:
$$ \frac{3 + x}{10 + x} = \frac{3}{4} $$

Cross-multiply to solve for $$ x $$:
$$ 4(3 + x) = 3(10 + x) $$
$$ 12 + 4x = 30 + 3x $$
$$ 4x - 3x = 30 - 12 $$
$$ x = 18 $$

**Conclusion:**
You need to add **18 blue marbles** to the bag to achieve the desired probability of $$ 75\% $$.

**Answer:**

**B. There must be 18 blue marbles added to the bag.**
You need to add 18 blue marbles to the bag to have a 75% chance of drawing a blue marble.

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