Tickets numbered from 1 to 20 are mixed thoroughly and then one ticket is drawn at random. What is the probability that the number on the drawn ticket is a multiple of 4 or a multiple of 15?

Introduction / Context:
This question uses simple probability with numbers on tickets. The event is defined in terms of divisibility by 4 or 15. To solve it correctly, we must count how many numbers in the range from 1 to 20 satisfy the divisibility condition and then divide by the total number of tickets.

Given Data / Assumptions:

• Tickets are numbered from 1 to 20 inclusive.
• One ticket is drawn at random.
• Each ticket has an equal chance of being chosen.
• Favourable tickets are those whose numbers are multiples of 4 or multiples of 15.

Concept / Approach:
We use the classical probability formula: probability equals number of favourable outcomes divided by total number of outcomes. For a condition of the form multiple of 4 or 15, we apply the union principle. Count multiples of 4, count multiples of 15, then subtract any common multiples to avoid double counting. Since the range is small, we can list multiples explicitly.

Step-by-Step Solution:
Total tickets = 20, so total outcomes = 20. Multiples of 4 between 1 and 20: 4, 8, 12, 16, 20. That is 5 numbers. Multiples of 15 between 1 and 20: 15 only. That is 1 number. Least common multiple of 4 and 15 is 60, which is greater than 20, so there is no overlap. Total favourable numbers = 5 + 1 = 6. Required probability = 6 / 20. Simplify 6 / 20 by dividing numerator and denominator by 2 to get 3 / 10.

Verification / Alternative check:
We can check by writing all numbers from 1 to 20 and marking those divisible by 4 or 15. The marked numbers are 4, 8, 12, 15, 16 and 20. Counting them gives 6 favourable tickets. Because there are 20 tickets total, the fraction 6 / 20 simplifies to 3 / 10, which confirms the previous calculation is correct.

Why Other Options Are Wrong:
1/4 would require exactly 5 favourable numbers, but there are 6. 2/5 corresponds to 8 favourable outcomes, which is too large for this range. 1/2 implies that 10 out of 20 numbers meet the condition, which clearly is not the case.

Common Pitfalls:
Some learners forget to check for common multiples of 4 and 15 and either subtract incorrectly or think there is an overlap when there is not. Others may miscount multiples of 4 by skipping 20 or including 0, which is outside the given range. Listing the numbers in the range and verifying each condition is a reliable method to avoid such mistakes.

Final Answer:
The probability that the drawn ticket shows a number that is a multiple of 4 or 15 is 3/10.