One number, n, is selected at random from a set of 10 integers. What is the probability that ½ n + 13 = 0 ?
1 .The largest integer in the set is 13.
2. The arithmetic mean of the set is zero.
For n/2+13 = 0, n = -26.
From F.S 1, we have the largest integer as 13. Thus the set could have all 10 positive integers including 13 in which case the probability - 0. Also, the number -26 could be included in some other combinations of 10 integers, where the probability would be a non-zero entity. Insufficient.
From F.S 2, as the arithmetic mean of the set is zero, hence the sum of all the ten integers is zero. Again, the presence/absence of -26 is not ascertained from this fact statement.Insufficient.
Combining both, for set -26,-5,-3,-2,0,2,4,8,9,13 --> the probability is 1/10
Again, for the set -13,-4,-3,-2,-1,1,2,3,4,13 --> the probability is 0. Insufficient.
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions