Question

Probability of getting at least one head in two coin tosses: ____.

• A. 1/4
• B. 1/2
• C. 3/4
• D. 1

Hint:

For "At least one" problems, the complement method ($1 - \text{None}$) is almost always faster, especially when dealing with 3 or more coins.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The sample space represents all possible outcomes. "At least one" means one or more.

Step 2: Key Formula or Approach:
Method 1: List favorable outcomes. Method 2: Use the complement rule: $P(\text{At least one}) = 1 - P(\text{None})$.

Step 3: Detailed Explanation:
1. Sample Space ($S$) for 2 coins: $\{HH, HT, TH, TT\}$. Total outcomes = 4. 2. Method 1: Favorable outcomes (At least one H) = $\{HH, HT, TH\}$. Count = 3. \[ P = \frac{3}{4} \] 3. Method 2: The only outcome with no heads is $\{TT\}$. \[ P(\text{None}) = \frac{1}{4} \] \[ P(\text{At least one}) = 1 - \frac{1}{4} = \frac{3}{4} \]

Step 4: Final Answer:
The probability is 3/4.