To solve this problem, we need to determine the probability of selecting one marble of each color (white, red, blue, and green) when four marbles are drawn randomly from a bag.

Step 1: Total number of marbles in the bag

The total number of marbles is:

$9 \, (\text{white}) + 11 \, (\text{red}) + 12 \, (\text{blue}) + 12 \, (\text{green}) = 44 \, \text{marbles}$

Step 2: Number of ways to select four marbles of different colors

To get one marble of each color (white, red, blue, and green), we must select:

• 1 white from the 9 white marbles,
• 1 red from the 11 red marbles,
• 1 blue from the 12 blue marbles,
• 1 green from the 12 green marbles.

The number of ways to select one marble from each color is:

$9 \times 11 \times 12 \times 12 = 14,256$

Step 3: Total number of ways to select any 4 marbles from 44

The total number of ways to choose 4 marbles out of 44 (without any restriction on colors) is given by the combination formula:

$\binom{44}{4} = \frac{44 \times 43 \times 42 \times 41}{4 \times 3 \times 2 \times 1} = 91,390$

Step 4: Probability calculation

The probability of selecting one marble of each color is the ratio of favorable outcomes to the total possible outcomes:

$P = \frac{14,256}{91,390} \approx 0.1560$

Step 5: Convert to percentage

To express this probability as a percentage, we multiply by 100:

$P \times 100 = 0.1560 \times 100 = 15.60\%$

Thus, the probability of grabbing one marble of each color is 15.60%.

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Do you want any details or have any questions?

Here are 5 related questions:

1. How would the probability change if the number of marbles of each color was different?
2. What is the probability of selecting exactly two red marbles and two blue marbles?
3. How would you calculate the probability of selecting at least one red marble?
4. What if we drew 5 marbles instead? How does this affect the calculation?
5. How would the probability be affected if one color of marble was unavailable?

Tip: When dealing with combinations, always make sure to distinguish between selection order (combinations) and arrangement (permutations).