A box contains 6 black balls and 4 green balls. Three balls were drawn in successive with replacement. What is the probability of getting three the same color?

To find the probability of drawing three balls of the same color with replacement, we need to consider the two possible outcomes: drawing three black balls or drawing three green balls.

### Step 1: Find the probability of drawing a black ball.
Since there are 6 black balls out of a total of 10 balls (6 black + 4 green), the probability of drawing a black ball on any draw is:
\[
P(\text{Black}) = \frac{6}{10} = 0.6
\]

### Step 2: Find the probability of drawing three black balls.
Since the draws are with replacement, the probability of drawing three black balls is:
\[
P(\text{Three Black}) = P(\text{Black}) \times P(\text{Black}) \times P(\text{Black}) = 0.6 \times 0.6 \times 0.6 = 0.216
\]

### Step 3: Find the probability of drawing a green ball.
Similarly, the probability of drawing a green ball is:
\[
P(\text{Green}) = \frac{4}{10} = 0.4
\]

### Step 4: Find the probability of drawing three green balls.
The probability of drawing three green balls is:
\[
P(\text{Three Green}) = P(\text{Green}) \times P(\text{Green}) \times P(\text{Green}) = 0.4 \times 0.4 \times 0.4 = 0.064
\]

### Step 5: Find the total probability of drawing three balls of the same color.
Since the events of drawing three black balls and three green balls are mutually exclusive, we add the probabilities:
\[
P(\text{Three Same Color}) = P(\text{Three Black}) + P(\text{Three Green}) = 0.216 + 0.064 = 0.28
\]

Thus, the probability of drawing three balls of the same color is **0.28** or **28%**.

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Would you like more details or further explanation? 

Here are 5 related questions for further practice:
1. What is the probability of getting exactly two black balls and one green ball?
2. What is the probability of getting no black balls?
3. How does the probability change if the draws are without replacement?
4. What is the expected number of black balls in three draws?
5. What is the probability of getting at least one green ball in three draws?

**Tip:** When dealing with "with replacement" problems, each draw is independent, meaning the probability of each event does not change after each draw.

A box contains 6 black balls and 4 green balls. Three balls were drawn in succession with replacement. What is the probability of getting three balls of the same color?

Learn how to calculate the probability of drawing three balls of the same color from a box containing 6 black and 4 green balls with replacement. The solution uses the multiplication rule of probability for independent events. Suitable for students in Grades 8-10.

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