Shiksha has 18 red balls and 9 green balls. She chooses a ball randomly. Find the probability that the chosen ball is of red colour.

Options

A. `4/5`
B. `1/3`
C. `3/5`
D. `2/3`

Answer

To find the probability that the chosen ball is of red color, we can follow these steps:

### Step 1: Identify the total number of balls.
Shiksha has 18 red balls and 9 green balls. To find the total number of balls, we add the number of red balls and green balls together.

\[ \text{Total number of balls} = \text{Number of red balls} + \text{Number of green balls} = 18 + 9 = 27 \]

### Step 2: Identify the number of favorable outcomes.
The favorable outcome in this case is choosing a red ball. The number of red balls is given as 18.

\[ \text{Number of favorable outcomes (red balls)} = 18 \]

### Step 3: Calculate the probability.
Probability is calculated using the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we have:

\[ \text{Probability of choosing a red ball} = \frac{18}{27} \]

### Step 4: Simplify the fraction.
To simplify \(\frac{18}{27}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 9.

\[ \frac{18 \div 9}{27 \div 9} = \frac{2}{3} \]

### Conclusion:
The probability that the chosen ball is of red color is \(\frac{2}{3}\).

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