12. If a number is selected at random from the list above, what is the probability that it will be less than 4?
Answer: B
The probability that a randomly selected number from the list will be less than 4 is 1/2.
In the given list (0, 1, 2, 3, 4, 5, 6, 7), the numbers that are less than 4 are 0, 1, 2, and 3. This results in 4 favorable outcomes out of a total of 8 numbers, leading to a probability of 4/8, which simplifies to 1/2.
A) 3/8
Option A is incorrect because the probability of selecting a number less than 4 is not represented by 3 favorable outcomes. There are actually 4 numbers (0, 1, 2, 3) that are less than 4, making this option inaccurate.
B) 1/2
Option B is correct as it accurately represents the probability of selecting a number less than 4. With 4 favorable outcomes (0, 1, 2, 3) out of 8 total numbers, the calculation results in 4/8, which simplifies to 1/2.
C) 5/8
Option C is incorrect because it suggests that there are 5 favorable outcomes for selecting a number less than 4. In reality, there are only 4 (0, 1, 2, 3), making this option an overestimation of the probability.
D) 3/4
Option D is also incorrect as it implies that 6 out of 8 outcomes are favorable. However, only 4 numbers are less than 4, thus misrepresenting the true probability.
Conclusion
The correct answer, 1/2, reflects the accurate calculation of favorable outcomes compared to total outcomes. All other options fail to represent the correct number of values less than 4, leading to erroneous probabilities. Hence, option B stands as the only valid choice based on the provided extract.