The outcomes of 5 tosses of a coin are recorded in a single sequence as H(head) and T(tail) for each toss. What is the number of elementary events in the sample space ?

Options

A. 5
B. 10
C. 25
D. 32

Explanation

To determine the number of elementary events in the sample space for the outcomes of 5 tosses of a coin, we can follow these steps:

### Step 1: Understand the Problem
When we toss a coin, there are two possible outcomes for each toss: Heads (H) or Tails (T). We need to find out how many different sequences can be formed when we toss the coin 5 times.

**Hint:** Think about the choices available for each individual toss.

### Step 2: Determine the Number of Outcomes for One Toss
For a single toss of a coin, there are 2 possible outcomes: H or T.

**Hint:** Consider how many outcomes are possible for just one toss.

### Step 3: Calculate the Total Outcomes for Multiple Tosses
Since each toss is independent of the others, the total number of outcomes for multiple tosses can be calculated using the formula:
\[ \text{Total Outcomes} = (\text{Number of Outcomes per Toss})^{\text{Number of Tosses}} \]

For 5 tosses:
\[ \text{Total Outcomes} = 2^5 \]

**Hint:** Remember that each toss contributes a factor of 2 to the total number of outcomes.

### Step 4: Perform the Calculation
Now, we calculate \( 2^5 \):
\[ 2^5 = 32 \]

**Hint:** You can break down the calculation if needed: \( 2^5 = 2 \times 2 \times 2 \times 2 \times 2 \).

### Step 5: Conclusion
Thus, the number of elementary events in the sample space when tossing a coin 5 times is 32.

**Final Answer:** The number of elementary events in the sample space is **32**.