Quote:
1000 numbers are generated. If you take every four numbers as a sequence then you have 250 possible sequences where you could have four even numbers. There are actually 997 potential sequences, but the 250 is a subset of the total that is easier to work with. So if the odds are minuscule that none of the 250 groups are all even, then it means that the odds are even more minuscule that none of the 997 groups are all even.
I think you are misunderstanding the question.
Quote:
2) 1000 random integers are generated randomly with a uniform distribution over the range 1 to 1000 inclusive. Which of the following would indicate a poor generator?
(a) the average of the numbers is about 499
(b) each number appears exactly once
(c) no four consecutive numbers are all even
(d) two of the above
(e) all of (a), (b), and (c)
My interpretation: we have 1000 random samples. Each sample can have a numeric value between 1 and 1000. When we say "four consecutive numbers" we intend to mean "four numbers in order of which they were generated" and not "four numbers in numeric order from least to greatest or greatest to least".