Final answer:
The probability of the range of a two-measurement sample being 6 from the given population {0, 1, 3, 4, 7} is 0.1, as only one viable pair exists (1,7).
Step-by-step explanation:
To calculate the probability that the range of a sample is 6 from the given population {0, 1, 3, 4, 7}, we first identify all possible pairs of numbers that can be drawn from the population. The pairs that have a range of 6 are (0,6) and (1,7). Next, we determine how many such pairs are in the full set of combinations. Since the order in which we draw the two numbers doesn't matter, we use combinations rather than permutations. There are a total of 10 unique pairs when choosing 2 numbers from 5 (as calculated by the binomial coefficient 5 choose 2), and there are only 1 pair that has a range of 6: (1,7), because the number 6 does not exist in the population.
Therefore, the probability that the two numbers chosen have a range of 6 is 1 out of 10, or 0.1. Thus, the chance of randomly selecting 1, 7 as the two-sample measurements is 10%