Let's analyze the problem step-by-step.

Problem Restatement

• A bag contains red and 10 white balls.
• A ball is drawn at random, its color is noted, and then it is replaced.
• This process is repeated 3 times.
• We want to find the probability that all 3 balls drawn are red.

Step 1: Define the variables

Let the number of red balls be rrr. Total balls in the bag = r+10r+10r+10.

Step 2: Probability of drawing a red ball in one draw

Since the ball is drawn at random,

P(red ball)=rr+10P(\text{red ball})=\frac{r}{r+10}P(red ball)=r+10r​

Step 3: Probability of drawing 3 red balls in 3 draws (with replacement)

Since the ball is replaced each time, the draws are independent. So,

P(3 red balls)=(rr+10)3P(\text{3 red balls})=\left(\frac{r}{r+10}\right)^3P(3 red balls)=(r+10r​)3

Summary

• If you know the number of red balls rrr, the probability that all 3 balls drawn are red is:

P=(rr+10)3\boxed{ P=\left(\frac{r}{r+10}\right)^3 }P=(r+10r​)3​

If you want, you can provide the exact number of red balls rrr, and I can calculate the numerical probability for you!