Question

Three coins are tossed together. The probability of getting exactly one head, is :

• A. \(\frac{1}{8}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{1}{2}\)
• D. \(\frac{3}{8}\)

Hint:

Using binomial expansion or combinations can speed up the calculation.
The number of ways to choose exactly \(1\) head from \(3\) tosses is given by \(\binom{3}{1} = 3\).
Since the total outcomes are \(2^3 = 8\), the probability is directly \(\frac{3}{8}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are analyzing a probability experiment where three fair coins are tossed simultaneously.
We need to calculate the probability that the outcome contains exactly one head.

Step 2: Key Formula or Approach:
The probability of an event \(E\) is defined as:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Step 3: Detailed Explanation:
1. Find the sample space \(S\) when three coins are tossed:
- Each coin has \(2\) possible outcomes (\(H\) or \(T\)).
- The total number of outcomes is \(2^3 = 8\).
- The sample space is:
\[ S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\} \] 2. Identify the favorable outcomes for the event \(E\) (getting exactly one head):
- Looking at the sample space, the outcomes containing exactly one \(H\) are:
\[ E = \{HTT, THT, TTH\} \] 3. Count the number of favorable outcomes:
- There are exactly \(3\) such outcomes.
4. Calculate the probability:
\[ P(E) = \frac{3}{8} \] 5. Thus, the probability of getting exactly one head is \(\frac{3}{8}\).

Step 4: Final Answer:
The correct option is (D).