In a survey of 700 investors, it was reported that 440 had invested in stocks, 384 had invested in bonds, and 87 had not invested in either stocks or bonds.

Exercise (a)
How many investors had invested in both stocks and bonds?

Part 1 of 3
Let S = {investors in stock} and B = {investors in bonds}.

Since there were a total of 700 investors and 87 of them had not invested in either stocks or bonds, the number investing in stocks or bonds is
n(S ∪ B)	 = 	700 −

=

We are given that there were 700 investors, and 87 had not invested in either stocks or bonds. So, the number of investors who invested in either stocks, bonds, or both is:

\[
n(S \cup B) = 700 - 87 = 613
\]

This represents the number of investors who invested in either stocks, bonds, or both.

Would you like further details or explanations? Here are some follow-up questions to consider:

1. What is the formula for finding the number of investors who invested in both stocks and bonds?
2. How do we calculate the number of investors who invested in only stocks?
3. What is the total number of investors who invested only in bonds?
4. How does the inclusion-exclusion principle apply to this scenario?
5. What happens if more investors start investing in both stocks and bonds?

**Tip:** Always keep track of totals when dealing with "either/or" situations using set notation or the inclusion-exclusion principle.

In a survey of 700 investors, it was reported that 440 had invested in stocks, 384 had invested in bonds, and 87 had not invested in either stocks or bonds. How many investors had invested in both stocks and bonds?

Learn how to solve a problem involving 700 investors where 440 invested in stocks, 384 invested in bonds, and 87 did not invest in either. This problem demonstrates the use of set theory and the inclusion-exclusion principle to find how many investors invested in both stocks and bonds. Suitable for students in Grades 9-11.

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