If a number from set M is selected at random, what is the probability that the number selected will be a factor of 12?

Rationale

The probability that a randomly selected number from set M is a factor of 12 is 0.4.

To determine this probability, we first need to identify the factors of 12, which are 1, 2, 3, 4, 6, and 12. If set M contains 15 numbers including these factors, the probability is calculated as the number of favorable outcomes (factors of 12) divided by the total outcomes (numbers in set M).

A (0.1) YOUR ANSWER

This probability suggests that only 10% of the numbers in set M are factors of 12. Given that there are 6 factors of 12, this choice underestimates the actual count of favorable outcomes, assuming a total of 60 numbers in set M, which is incorrect.

B (0.2) YOUR ANSWER

A probability of 0.2 implies that 20% of the numbers in set M are factors of 12. This would mean there are only 3 factors identified out of a total of 15 numbers, which is inaccurate as there are 6 factors of 12 present.

C (0.4) CORRECT

This is the correct answer, representing the scenario where 6 out of 15 numbers in set M are factors of 12. The calculation is 6 (factors of 12) divided by 15 (total numbers), yielding 0.4 or 40% probability.

D (0.5) YOUR ANSWER

This probability indicates that half of the numbers in set M are factors of 12, which would imply that there are 7.5 factors, an impossible scenario. Since there are only 6 factors, this option overestimates the proportion of favorable outcomes.

Conclusion

To summarize, the probability of selecting a factor of 12 from set M, which contains 15 numbers, is accurately represented by 0.4 as there are 6 favorable outcomes. The other choices fail to reflect the actual number of factors or miscalculate the total numbers in set M, reinforcing the importance of understanding basic probability principles in such contexts.