A bag containing 5 red and 4 black balls. If a ball is drawn at random from the bag, what is the probability of getting a black ball.

Options

A. `4/9`
B. `9/4`
C. `5/2`
D. `2/5`

Answer

To solve the problem of finding the probability of drawing a black ball from a bag containing 5 red and 4 black balls, we can follow these steps:

### Step 1: Determine the total number of balls in the bag.
- We have 5 red balls and 4 black balls.
- Total number of balls = Number of red balls + Number of black balls
- Total number of balls = 5 + 4 = 9

### Step 2: Identify the number of favorable outcomes.
- The favorable outcome in this case is drawing a black ball.
- The number of black balls (favorable outcomes) = 4

### Step 3: Use the probability formula.
- The formula for probability is given by:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes is 4 (black balls) and the total number of outcomes is 9 (total balls).

### Step 4: Substitute the values into the formula.
- Probability of getting a black ball = \(\frac{4}{9}\)

### Step 5: State the final answer.
- Therefore, the probability of drawing a black ball from the bag is \(\frac{4}{9}\).

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