In a blood donation camp, 1345 people gave blood and 247 of them were found to have high blood pressure. What is the probability that a randomly selected person from this group did not have high blood pressure?

Introduction / Context:
This question is from basic probability and statistics, using a real life context of a blood donation camp. Out of a total number of donors, some have high blood pressure and the rest do not. The task is to find the probability that a randomly chosen donor from this group does not have high blood pressure. Such questions test understanding of simple probability based on counts of favourable and total outcomes.

Given Data / Assumptions:
- Total number of people who gave blood = 1345.
- Number of people with high blood pressure = 247.
- The rest of the donors are assumed not to have high blood pressure.
- The selection of one person is random, so each donor is equally likely to be chosen.
- We are asked for the probability that the chosen person does not have high blood pressure.

Concept / Approach:
Probability of an event is defined as:
P(event) = number of favourable outcomes / total number of possible outcomes.
Here, the event of interest is that a randomly chosen donor does not have high blood pressure. Therefore, the favourable outcomes are the donors who do not have high blood pressure. We first compute that number by subtracting the number with high blood pressure from the total. Then we divide the favourable count by the total population of donors. Expressing the answer as a fraction is a common and exact way to present probabilities in such questions.

Step-by-Step Solution:
Step 1: Write the total number of donors as 1345. Step 2: Write the number of donors with high blood pressure as 247. Step 3: Compute the number of donors without high blood pressure by subtraction: 1345 - 247 = 1098. Step 4: The favourable outcomes are donors without high blood pressure, so the favourable count is 1098. Step 5: Use the probability formula: P(no high blood pressure) = favourable outcomes / total outcomes = 1098 / 1345. Step 6: The fraction 1098/1345 is already in simplest form, so this is the exact probability. In decimal form this is approximately 0.816, which is about 0.82.

Verification / Alternative check:
We can verify using the complement rule. The probability of high blood pressure is 247/1345. The complement event, no high blood pressure, should have probability 1 - 247/1345. Compute this as:
1 - 247/1345 = (1345/1345) - (247/1345) = (1345 - 247)/1345 = 1098/1345. This matches the earlier result, confirming that 1098/1345 is correct.

Why Other Options Are Wrong:
247/1345: This is the probability that a donor has high blood pressure, not that they are free from it.
1345/1098: This is the reciprocal of the correct fraction and cannot represent a probability since it is greater than 1.
247/1098: This uses the wrong denominator and does not match any correct probability derived from the data.

Common Pitfalls:
A common mistake is to confuse the count with high blood pressure with the count without it, leading to choosing 247/1345 instead of the complement. Another frequent error is to forget to subtract and directly divide one given number by another without thinking about the event definition. Students should clearly decide which outcome is favourable and which is total before forming the probability fraction. Misinterpreting the complement rule or trying to invert the fraction also leads to incorrect answers greater than 1, which can never be valid probabilities.

Final Answer:
Therefore, the probability that a randomly selected donor from this group did not have high blood pressure is 1098/1345.