A box contains 5 red balls , 8 green balls and 10 pink balls . A ball is drawn at random from the box. Find the probability that the ball drawn is either red or green.

Options

A. A)`(13)/(23)`
B. B)`(10)/(23)`
C. C)`(11)/(23)`
D. D)`(13)/(529)`

Answer

To find the probability that a ball drawn from the box is either red or green, we can follow these steps:

### Step 1: Determine the total number of balls in the box.
- The box contains:
- 5 red balls
- 8 green balls
- 10 pink balls

**Total number of balls = Number of red balls + Number of green balls + Number of pink balls**
\[ \text{Total number of balls} = 5 + 8 + 10 = 23 \]

### Step 2: Determine the number of favorable outcomes.
- The favorable outcomes are the number of balls that are either red or green.
- Number of red balls = 5
- Number of green balls = 8

**Total favorable outcomes = Number of red balls + Number of green balls**
\[ \text{Total favorable outcomes} = 5 + 8 = 13 \]

### Step 3: Calculate the probability.
- Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes is 13 and the total number of outcomes is 23.

**So, the probability that the ball drawn is either red or green is:**
\[ \text{Probability} = \frac{13}{23} \]

### Final Answer:
The probability that the ball drawn is either red or green is \(\frac{13}{23}\).

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