There are 5 red and 7 white balls in a bag. Find the probability that none ball is red ?

Answer

To solve the problem of finding the probability that none of the balls drawn from a bag containing 5 red and 7 white balls is red, we can follow these steps:

### Step 1: Identify the total number of balls
First, we need to determine the total number of balls in the bag. There are 5 red balls and 7 white balls.

\[ \text{Total number of balls} = \text{Number of red balls} + \text{Number of white balls} = 5 + 7 = 12 \]

### Step 2: Identify the favorable outcomes
Next, we need to identify the favorable outcomes for the event that no ball drawn is red. Since we want none of the balls to be red, we can only draw from the white balls.

\[ \text{Number of favorable outcomes (white balls)} = 7 \]

### Step 3: Calculate the probability
The probability of an event is calculated using the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the probability that none of the balls drawn is red can be calculated as follows:

\[ \text{Probability (no red balls)} = \frac{\text{Number of favorable outcomes}}{\text{Total number of balls}} = \frac{7}{12} \]

### Final Answer
Thus, the probability that none of the balls drawn is red is:

\[ \frac{7}{12} \]

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