A bag contains 2 white marbles, 4 blue marbles and 6 red marbles. Three marbles are drawn from the bag . What is the probability that
none is black ?

Answer

To solve the problem step by step, we need to determine the probability that none of the marbles drawn from the bag is black.

### Step 1: Identify the total number of marbles in the bag.
- We have:
- 2 white marbles
- 4 blue marbles
- 6 red marbles

Calculating the total:
\[ \text{Total marbles} = 2 + 4 + 6 = 12 \]

### Step 2: Identify the number of black marbles.
- According to the problem, there are **0 black marbles** in the bag.

### Step 3: Define the event of drawing a black marble.
- Let event \( B \) be defined as drawing a black marble.
- The number of black marbles, \( n(B) = 0 \).

### Step 4: Calculate the probability of drawing a black marble.
- The probability of event \( B \) (drawing a black marble) can be calculated as:
\[ P(B) = \frac{n(B)}{\text{Total marbles}} = \frac{0}{12} = 0 \]

### Step 5: Calculate the probability of the complement event (none is black).
- The complement of event \( B \) is denoted as \( B' \) (none is black).
- The probability of none being black is given by:
\[ P(B') = 1 - P(B) = 1 - 0 = 1 \]

### Conclusion:
- Therefore, the probability that none of the marbles drawn is black is:
\[ \text{Probability (none is black)} = 1 \]