Question

Out of 28 students, 12 have at least one brother and 13 have at least one sister. 8 students have both brothers and sisters. How many students do not have either a brother or a sister?

Answer 1

The answer is 11

Explanation:

brother only=12-8=4

sister only=13-8=5

brother and sister =8

neither of them=x

28=4+8+5+x

28=17+x

x=28-17

x=11

Answer 2

11

Explanation:

You want to know the number of students with no brother or sister, given that 12 of 28 have at least one brother, 13 have at least one sister, and 8 have both.

Two-way table

The attachment shows the two-way table that can be formed from the given information. The four given numbers are shown in green at lower right. The other numbers in the table are filled in to make the totals accurate.

The number of students not having either a brother or sister is 11.

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Additional comment

In terms of probability, which is the fraction that each event is of the total, you have ...

P(B∪S) = P(B) +P(S) -P(B∩S) . . . . . . . useful relation to memorize

P(B'∩S') = 1 -P(B∪S) = 1 -(12/28 +13/28 -8/28) = 11/28

This tells you 11 of the 28 students do not have a brother or sister.

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