A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space thise experiment.

Explanation

To find the sample space for the experiment of drawing two balls from a box containing 1 red ball and 3 identical white balls without replacement, we can follow these steps:

### Step 1: Identify the Balls
We have:
- 1 Red ball (denote as R)
- 3 Identical White balls (denote as W)

### Step 2: Understand the Drawing Process
Since we are drawing two balls in succession without replacement, it means that once we draw a ball, we do not put it back into the box.

### Step 3: Determine Possible Outcomes
We will consider the different scenarios based on the order of drawing the balls:

1. **First Ball is Red (R)**:
- If the first ball drawn is Red (R), the second ball can only be White (W) because there are no more Red balls left.
- This gives us the outcome: **(R, W)**

2. **First Ball is White (W)**:
- If the first ball drawn is White (W), there are two possibilities for the second ball:
- The second ball can be Red (R).
- The second ball can also be White (W) (since we have 3 identical white balls).
- This gives us the outcomes: **(W, R)** and **(W, W)**

### Step 4: Compile the Sample Space
Now, we can compile all the possible outcomes from the above scenarios:
- (R, W)
- (W, R)
- (W, W)

Thus, the sample space \( S \) for this experiment is:
\[ S = \{ (R, W), (W, R), (W, W) \} \]

### Final Answer
The sample space for the experiment of drawing two balls from the box is:
\[ S = \{ (R, W), (W, R), (W, W) \} \]

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