Question

The probability of getting heads on both the coins in throwing two coins is

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

Hint:

For independent events like coin tosses, you can also multiply their individual probabilities. The probability of getting a head on one coin is 1/2. The probability of getting heads on both is \(1/2 \times 1/2 = 1/4\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem asks for the probability of a specific outcome when two coins are tossed simultaneously. We need to identify all possible outcomes and then find the ones that match the desired event.

Step 2: Key Formula or Approach:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \]

Step 3: Detailed Explanation:
When two coins are tossed, the set of all possible outcomes (the sample space) is:
\{HH, HT, TH, TT\}
where H = Heads and T = Tails.
The total number of possible outcomes is 4.
The event we are interested in is "getting heads on both the coins."
The favorable outcome for this event is just one: \{HH\}.
The number of favorable outcomes is 1.
Now, calculate the probability:
\[ P(\text{both heads}) = \frac{1}{4} \]

Step 4: Final Answer:
The probability is \(\frac{1}{4}\).