SOLUTION: A survey of 45 students found that 30 to take Spanish and 40 take algebra. What is the fewest possible number of students surveyed who are taking both Spanish and algebra? And in t

Question 1064329: A survey of 45 students found that 30 to take Spanish and 40 take algebra. What is the fewest possible number of students surveyed who are taking both Spanish and algebra? And in the answer I will need to know how we get to that answers because I'd like to learn
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Number taking S=30
Number taking A=40
There has to be overlap, or there would be 70 students. There are only 45
Number taking both = at least 25, the minimum.
When you have p(A)+p(B), and there is no overlap, the probability of OR is their sum. The probability of AND is 0, because there is no overlap. If there is overlap, you are double counting them, so the probability of both (AND) has to be accounted for.
Here, there can't be more than 45 students. It is possible 30 are taking both. It can't be more, or the number taking Spanish would be higher. It could also be 29...25. It can't be lower than 25, otherwise when we subtract the double counting, we would end up with more students than we started.

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