Question

In a simultaneous toss of two coins, the probability of getting at least one head is

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

Answer 1

The Correct Option is B

Step 1: List all possible outcomes.

When two coins are tossed, the possible outcomes are:

\[ \{HH, HT, TH, TT\}, \]

where \(H\) represents heads and \(T\) represents tails. Thus, there are 4 possible outcomes.

Step 2: Identify favorable outcomes for "at least one head".

The event "at least one head" includes all outcomes where one or both coins show heads. These outcomes are:

\[ \{HH, HT, TH\}. \]

There are 3 favorable outcomes.

Step 3: Compute the probability.

The probability is the ratio of favorable outcomes to total outcomes:

\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{3}{4}. \]

Final Answer: The probability of getting at least one head is \( \mathbf{\frac{3}{4}} \), which corresponds to option \( \mathbf{(2)} \).