Math Problem Statement

In a bag, there are 12 identical tokens numbered from 1 to 12. A token is drawn at random. What is the probability to obtain an even multiple of 3?

Solution

Problem:

We are tasked with finding the probability of obtaining an even multiple of 3 when randomly selecting one token from a bag of 12 tokens, numbered from 1 to 12.

Step 1: Identify the even multiples of 3 between 1 and 12.

  • Multiples of 3: 3,6,9,123, 6, 9, 12.
  • Even multiples of 3: 6,126, 12.

Thus, the even multiples of 3 are 66 and 1212.

Step 2: Calculate the probability.

  • Total tokens = 1212.
  • Favorable outcomes (even multiples of 3) = 22.

The probability PP is calculated as: P=Number of favorable outcomesTotal number of outcomes=212=16.P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{12} = \frac{1}{6}.

Final Answer:

The probability of obtaining an even multiple of 3 is 16\frac{1}{6} (Answer D).


Do you have any questions, or would you like a detailed explanation of a specific step?

Here are 5 related questions to expand your understanding:

  1. How can we determine all multiples of a specific number within a given range?
  2. How do we generalize the concept of probability to other scenarios?
  3. What is the probability of selecting an odd multiple of 3 from the same set?
  4. Can we extend this method to non-consecutive numbering, such as tokens labeled with random numbers?
  5. How would the answer change if there were 24 tokens numbered 1 to 24?

Tip: Always list all possible outcomes carefully to ensure you count the favorable outcomes accurately in probability problems.

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Math Problem Analysis

Mathematical Concepts

Probability
Multiples
Divisibility

Formulas

P = Favorable outcomes / Total outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8