An experiment consists of tossing four fair coins independently. The outcome of the experiment is considered favourable, if the number of heads is greater than the number of tails. The probability of a favourable outcome from a single experiment is

Correct option is C

Concept:

The problem involves calculating the probability of a favorable outcome when tossing four fair coins. A favorable outcome occurs when the number of heads is greater than the number of tails. The probability is calculated as:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Solution:

Step 1: Total Number of Outcomes
Each coin toss has two possible outcomes: Head (H) or Tail (T). Since four coins are tossed independently, the total number of possible outcomes is:

Total outcomes = 2⁴ = 16.

A favorable outcome occurs when the number of heads is greater than the number of tails.

In 4 coin tosses, we need 3 heads and 1 tail, or 4 heads and 0 tails.

The number of ways to choose 3 heads from 4 tosses is given by (4, 3) = 4 and there is only 1 way to get 4 heads, i.e., HHHH .

Thus, the total number of favorable outcomes is 

4 (for 3 heads, 1 tail) + 1 (for 4 heads) = 5 favorable outcomes.
The probability is the ratio of favorable outcomes to total outcomes P(Favorable) = 5/16.

The probability of a favorable outcome is Option c .