Three fair coins are tossed simultaneously. What is the probability of getting more heads than tails in the outcome?

Introduction / Context:
This probability question deals with tossing three fair coins at the same time. The requirement more heads than tails means that the number of heads in the result must be strictly greater than the number of tails. With three coins, this condition leads to a small set of favourable outcomes, which we can identify by listing the sample space systematically.

Given Data / Assumptions:

• There are three unbiased coins.
• Each coin has two possible results: head (H) or tail (T).
• All 2^3 = 8 possible outcomes of the three tosses are equally likely.
• More heads than tails means heads count greater than tails count.

Concept / Approach:
For three coins, the number of heads can be 0, 1, 2 or 3. More heads than tails requires heads count greater than tails count. If there are 0 heads, tails are 3, so this is not allowed. If there is 1 head, then tails equal 2, still not allowed. If there are 2 heads, tails are 1 and the condition is satisfied. If there are 3 heads, tails are 0 and the condition is also satisfied. We therefore count outcomes with either 2 heads or 3 heads and divide by the total of 8 outcomes.

Step-by-Step Solution:
List all outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Outcomes with 2 heads and 1 tail: HHT, HTH, THH, which gives 3 outcomes. Outcome with 3 heads and 0 tails: HHH, which gives 1 outcome. Total favourable outcomes where heads are more than tails = 3 + 1 = 4. Total possible outcomes = 8. Required probability = 4 / 8 = 1 / 2.

Verification / Alternative check:
We can also use symmetry. For three coins, the distribution of heads is symmetric around 1.5. Exactly half of the outcomes have more heads than tails and half have more tails than or equal number of heads when carefully grouped. Counting confirms that 4 out of 8 outcomes meet the condition, which supports the conclusion that the probability is 1 / 2.

Why Other Options Are Wrong:
5/8 would require 5 favourable outcomes, which is more than the 4 that satisfy the condition. 7/8 suggests that almost every outcome has more heads than tails, which is clearly not true when we list them. 3/8 would mean only 3 favourable cases, while we identified 4 outcomes that work.

Common Pitfalls:
Learners sometimes misinterpret more heads than tails as at least two heads, then forget to include the case of three heads or miscount the number of sequences with two heads. Another frequent mistake is not listing the full sample space and missing one or more outcomes. Writing down all eight possibilities for three coins is quick and ensures complete coverage before counting the favourable ones.

Final Answer:
The probability of getting more heads than tails when three fair coins are tossed is 1/2.