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. \(\frac{3}{8}\)

Hint:

Probability of exactly \(k\) successes in \(n\) trials = \(\binom{n}{k} \times (p)^k \times (1-p)^{n-k}\). For fair coins, \(p = \frac{1}{2}\).

Answer 1

The Correct Option is D

Given:
Three coins are tossed together.

To find:
Probability that exactly one coin shows head.

Step 1: Total number of possible outcomes
Each coin has 2 possible outcomes (Head or Tail).
So, total outcomes = \(2^3 = 8\).

Step 2: Number of favorable outcomes (exactly one head)
Possible outcomes with exactly one head are:
- 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:
\[ \boxed{\frac{3}{8}} \]