Question 10

The probability that the number selected will be a factor of 12 is 0.4.

The number of factors of 12 is 6: {1, 2, 3, 4, 6, 12}. If set M contains a total of 15 numbers, the probability that a randomly selected number from set M will be a factor of 12 is calculated as the number of favorable outcomes divided by the total outcomes, which equals 6/15 or 0.4.

A) 0.1

This option represents a probability that suggests only 1 out of 10 numbers in set M is a factor of 12. Given that there are 6 factors of 12, this probability is incorrect as it underestimates the likelihood significantly.

B) 0.2

This option indicates a probability of 2 out of 10 numbers being factors of 12. However, with 6 factors of 12 present in the set, this probability also fails to accurately reflect the situation, making it incorrect.

C) 0.4

This option correctly states the probability that a number selected from set M is a factor of 12. With 6 factors of 12 out of a total of 15 numbers in the set, the calculation yields a probability of 6/15, which simplifies to 0.4, validating this choice as correct.

D) 0.5

This option suggests a probability of half the numbers in set M being factors of 12, which implies that 7.5 out of 15 numbers would need to be factors. Since there are only 6 factors of 12, this estimate is inaccurate and therefore incorrect.

Conclusion

The correct probability of 0.4 accurately reflects the ratio of factors of 12 to the total numbers in set M. All other options misrepresent the likelihood by either underestimating or overestimating the number of factors present, confirming that option C is the only appropriate choice.