Avni and Arushi draws one ball each from a bag containing 2 red and 3 green balls. Avni draws a red ball first which is not put back. What is the probability that Arushi who draws next also gets a red ball?

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the initial contents of the bag.
The bag contains:
- 2 red balls
- 3 green balls

Total number of balls = 2 (red) + 3 (green) = 5 balls.

### Step 2: Determine the situation after Avni draws a red ball.
Avni draws one red ball from the bag, and since it is not put back, the contents of the bag change. After Avni's draw:
- Red balls left = 2 - 1 = 1 red ball
- Green balls left = 3 (remains unchanged)

Now, the total number of balls left in the bag = 1 (red) + 3 (green) = 4 balls.

### Step 3: Calculate the probability that Arushi draws a red ball.
Now, Arushi will draw from the remaining balls. The probability of drawing a red ball can be calculated using the formula:

\[ \text{Probability of drawing a red ball} = \frac{\text{Number of red balls left}}{\text{Total number of balls left}} \]

Substituting the values we have:
\[ \text{Probability of drawing a red ball} = \frac{1 \text{ (red ball)}}{4 \text{ (total balls)}} = \frac{1}{4} \]

### Final Answer:
The probability that Arushi also gets a red ball is \(\frac{1}{4}\).

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