Question

Three coins are tossed together. The probability that exactly one coin shows head, is

• A. \( \frac{1}{8} \)
• B. \( \frac{1}{4} \)
• C. 1
• D. \( \frac{3}{8} \)

Answer 1

The Correct Option is D

Given:
- Three coins are tossed together.
- We need to find the probability that exactly one coin shows a head.

Step 1: Find total number of possible outcomes
Each coin has 2 possible outcomes: Head (H) or Tail (T).
Total outcomes for 3 coins: \[ 2 \times 2 \times 2 = 8 \] These outcomes are: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.

Step 2: Identify favorable outcomes (exactly one head)
Favorable outcomes are those with exactly one head:
- HTT
- THT
- TTH
Number of favorable outcomes = 3.

Step 3: Calculate probability
\[ P(\text{exactly one head}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{8} \]

Final Answer:
\[ \boxed{\frac{3}{8}} \]