A bag contains 3 black marbles, 5 red marbles and 6 white marbles. If a marble is picked at random, then what is the probability that it is not a white marble?

Answer

To find the probability that a marble picked at random from the bag is not a white marble, we can follow these steps:

### Step 1: Identify the number of each color marble
- Black marbles = 3
- Red marbles = 5
- White marbles = 6

### Step 2: Calculate the total number of marbles
To find the total number of marbles in the bag, we add the number of black, red, and white marbles together:
\[ \text{Total marbles} = \text{Number of black marbles} + \text{Number of red marbles} + \text{Number of white marbles} \]
\[ \text{Total marbles} = 3 + 5 + 6 = 14 \]

### Step 3: Determine the number of marbles that are not white
To find the number of marbles that are not white, we add the number of black and red marbles:
\[ \text{Number of marbles not white} = \text{Number of black marbles} + \text{Number of red marbles} \]
\[ \text{Number of marbles not white} = 3 + 5 = 8 \]

### Step 4: Calculate the probability of picking a marble that is not white
The probability \( P \) of an event is given by the formula:
\[ P(\text{not white}) = \frac{\text{Number of marbles not white}}{\text{Total number of marbles}} \]
Substituting the values we found:
\[ P(\text{not white}) = \frac{8}{14} \]

### Step 5: Simplify the fraction
To simplify \( \frac{8}{14} \), we divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[ P(\text{not white}) = \frac{8 \div 2}{14 \div 2} = \frac{4}{7} \]

### Final Answer:
The probability that a marble picked at random is not a white marble is \( \frac{4}{7} \).

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