Rationale
The probability that a randomly selected number from the list will be less than 4 is 1/2.
In the list provided (0, 1, 2, 3, 4, 5, 6, 7), there are four numbers (0, 1, 2, and 3) that are less than 4 out of a total of eight numbers. Therefore, the probability is calculated as the number of favorable outcomes over the total outcomes, resulting in 4/8, which simplifies to 1/2.
A) 3/8
This choice suggests that only three numbers are less than 4, which is incorrect. There are actually four numbers (0, 1, 2, and 3) that meet this criterion. Thus, the probability of selecting a number less than 4 is overestimated with this option.
B) 1/2
This option accurately represents the probability of selecting a number less than 4 from the list. With four favorable outcomes (0, 1, 2, and 3) out of eight possible outcomes, the probability simplifies correctly to 1/2.
C) 5/8
This choice indicates that five numbers are less than 4, which is not the case. There are only four numbers below 4, making this choice an overestimation of the favorable outcomes.
D) 3/4
This option implies that three-quarters of the numbers in the list are less than 4. However, only four out of eight numbers meet the condition, making this calculation incorrect.
Conclusion
The probability of selecting a number less than 4 from the list is correctly identified as 1/2, based on the ratio of favorable outcomes to total outcomes. The other options either overestimate or underestimate the count of numbers below 4, reinforcing the importance of accurately counting favorable conditions in probability assessments.
