In a group of 50 students: - 20 like hiking - 25 like biking - 10 like both How many like either hiking or biking?

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BlackTom AI · Accepted Answer

Start by identifying what the question is asking: the number of students who like either hiking or biking (the union of the two groups).
Option 1 (a. 55): If we add the counts 20 (hiking) and 25 (biking), we get 45, but we have double-counted those who like both; adding 20 and 25 to get 45 ignores the overlap, so 55 is not possible here.
Option 2 (b. 45): 20 + 25 equals 45, which would be the total if there were no overlap between the groups. Since there are students who like both (the intersection), the union must be less than 45, not equal to it. Therefore 45 overcounts the total.
Option 3 (c. 30): This would imply that the overlap is larger than given. Using the inclusion–exclusion principle, |H ∪ B| = |H| + |B| − |H ∩ B|. With |H| = 20, |B| = 25, and |H ∩ B| = 10, the union is 20 + 25 − 10 = 35, not 30. So 30 undercounts the true union.
Option 4 (d. 35): Apply the standard formula for the union of two sets: |H ∪ B| = |H| + |B| − |H ∩ B|. Substituting the given values, 20 + 25 − 10 = 35. This aligns with the inclusion–exclusion principle, accounting correctly for the overlap of 10 students who like both activities.
In summary, the correct computation is 20 + 25 − 10 = 35, which corresponds to option d. 35.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

In a group of 50 students: - 20 like hiking - 25 like biking - 10 like both How many like either hiking or biking?

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