In a lottery there are 10 prize tickets and 25 blank tickets, making 35 tickets in total.\nOne ticket is drawn at random.\nWhat is the probability that the ticket drawn is a prize ticket?

Introduction / Context:
This question is a straightforward probability problem involving a simple lottery. You need to calculate the probability of drawing a prize ticket when the total number of prize and blank tickets is known.

Given Data / Assumptions:

• Number of prize tickets = 10.
• Number of blank tickets = 25.
• Total number of tickets = 10 + 25 = 35.
• One ticket is drawn at random.
• All tickets are equally likely to be drawn.
• The event of interest is drawing a prize ticket.

Concept / Approach:
We apply the basic probability formula: Probability = number of favourable outcomes / total number of outcomes. Here, the favourable outcomes are the prize tickets, and the total outcomes are all tickets in the lottery. Because each ticket is equally likely, we just take the ratio of counts.

Step-by-Step Solution:
Total tickets = 35. Prize tickets = 10. Probability of a prize = 10 / 35. Simplify 10 / 35 by dividing numerator and denominator by 5. 10 / 35 = 2 / 7. So the probability of drawing a prize ticket is 2/7.

Verification / Alternative check:
We can also look at the probability of drawing a blank ticket which is 25 / 35 = 5 / 7. The probabilities of prize and blank must sum to 1. Indeed, 2/7 + 5/7 = 1. This consistency check confirms our calculation.

Why Other Options Are Wrong:
Option 1/7 would be correct if there were only 5 prizes out of 35. Option 3/7 would require 15 prize tickets, which we do not have. Option 2/5 corresponds to 14 prize tickets out of 35, which is again incorrect.

Common Pitfalls:
A typical mistake is to forget to include both prize and blank tickets when counting the total. Another error is to mis-simplify fractions, for example reducing 10/35 incorrectly. Always double check that the numerator reflects favourable outcomes and that the denominator is the total number of possible outcomes.

Final Answer:
The probability of getting a prize ticket is 2/7.