Question

A bag contains 3 blue 5 red 4 green and 2 white balls. Find the chance of drawing at random one ball without replacement which is not white

Answer 1

To find the probability of drawing a ball that is not white from the bag, we first need to determine the total number of balls and the number of non-white balls.

### Step 1: Count the total number of balls
- Blue balls: 3
- Red balls: 5
- Green balls: 4
- White balls: 2

**Total number of balls:**
\[
3 + 5 + 4 + 2 = 14
\]

### Step 2: Calculate the number of non-white balls
The non-white balls are blue, red, and green:
- Blue: 3
- Red: 5
- Green: 4

**Total non-white balls:**
\[
3 + 5 + 4 = 12
\]

### Step 3: Calculate the probability of drawing a non-white ball
The probability \( P \) of an event is given by the formula:
\[
P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the favorable outcomes are drawing a non-white ball, and the total outcomes are drawing any ball.

Thus, the probability of drawing a non-white ball is:
\[
P(\text{not white}) = \frac{\text{Number of non-white balls}}{\text{Total number of balls}} = \frac{12}{14}
\]

### Step 4: Simplify the fraction
\[
P(\text{not white}) = \frac{12}{14} = \frac{6}{7}
\]

Therefore, the chance of drawing one ball that is not white is \(\frac{6}{7}\).