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 \(\frac{6}{7}\).
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