平成27年度 秋期 ITパスポート試験 問87

※ Our check while writing this explanation could not fully confirm the published answer; scoring follows IPA's official key.

• ×Incorrectア

  49 is not the union; it corresponds to counting only one exclusive region — where only one of the items is 2 or lower (and the other does not apply). Since the targets are either one or both, i.e. the whole union, counting only a single region falls far short.

• ○イ

  正解 The targets of the follow-up survey are the customers who answered a rating of 2 or lower (somewhat dissatisfied / dissatisfied) to either one or both of the store and the guide/pamphlet — that is, the union of the two sets. The size of the union is found by the inclusion-exclusion principle: (number rating the store 2 or lower) + (number rating the guide/pamphlet 2 or lower) − (number rating both 2 or lower). In terms of a Venn diagram, simply adding the two circles counts the overlapping part twice, so the overlap (both 2 or lower = 38 people) must be subtracted exactly once. The total of the applicable counts for the two items is 164 people, and subtracting the duplicated 38 people gives 164−38=126, so there are 126 targets. Therefore the correct answer is イ.

• ×Incorrectウ

  162 comes from the right idea of subtracting the overlap but subtracts the wrong amount (it does not subtract exactly 38 once); it is a near-miss wrong answer. Correctly, subtract the overlapping 38 from the total 164 to get 126.

• ×Incorrectエ

  164 is merely the simple sum of the applicable counts for the two items (store 2 or lower + guide/pamphlet 2 or lower). It double-counts the 38 people who are 2 or lower on both, a typical mistake of failing to subtract the overlap. Correctly, 164−38=126.