Describe the Sample Space for the experiment:
A coin is tossed. If it shows head, we draw a ball from a bag consisting of 2 red and 3 black balls. If it shows tail, coin is tossed again.

Answer

To describe the sample space for the given experiment, we will follow these steps:

### Step 1: Identify the outcomes of the first coin toss
When we toss a coin, there are two possible outcomes:
- Heads (H)
- Tails (T)

### Step 2: Determine the actions based on the first outcome
- If the outcome is Heads (H), we will draw a ball from a bag that contains 2 red balls and 3 black balls. The possible outcomes when drawing a ball are:
- Red Ball 1 (R1)
- Red Ball 2 (R2)
- Black Ball 1 (B1)
- Black Ball 2 (B2)
- Black Ball 3 (B3)

Thus, the outcomes after getting Heads are:
- H, R1
- H, R2
- H, B1
- H, B2
- H, B3

- If the outcome is Tails (T), we will toss the coin again. The possible outcomes for the second toss are again:
- Heads (H)
- Tails (T)

### Step 3: Determine the outcomes based on the second toss
- If the second toss results in Heads (H), the outcomes will be:
- T, H (and we don't draw a ball in this case)

- If the second toss results in Tails (T), the outcomes will be:
- T, T (and we also don't draw a ball in this case)

### Step 4: Combine all outcomes to form the sample space
Now, we can combine all the outcomes from both scenarios to form the complete sample space (S):
- From the first toss being Heads:
- S = { (H, R1), (H, R2), (H, B1), (H, B2), (H, B3) }
- From the first toss being Tails:
- S = { (T, H), (T, T) }

### Final Sample Space
Combining both parts, the complete sample space is:
- S = { (H, R1), (H, R2), (H, B1), (H, B2), (H, B3), (T, H), (T, T) }