Question

In a survey conducted by Helena, a financial consultant, it was revealed of her 411 clients 285 own stocks, 179 own bonds, 180 own mutual funds, 115 own both stocks and bonds, 100 own both stocks and mutual funds, 95 own both bonds and mutual funds. How many of Helena's clients own stocks, bonds, and mutual funds?

Options:
a. 35
b. 45
c. 55
d. 65

Answer 1

To find out how many of Helena's clients own stocks, bonds, and mutual funds, we can use a Venn diagram. By subtracting the number of clients who own both pairs of investments and adding back the number of clients who own all three, we find that 310 of Helena's clients own stocks, bonds, and mutual funds.

Step-by-step explanation:

To find out how many of Helena's clients own stocks, bonds, and mutual funds, we can use a Venn diagram. Let's start by filling in the information we have:

• Total number of clients (n) = 411
• Number of clients who own stocks (S) = 285
• Number of clients who own bonds (B) = 179
• Number of clients who own mutual funds (M) = 180
• Number of clients who own both stocks and bonds = 115
• Number of clients who own both stocks and mutual funds = 100
• Number of clients who own both bonds and mutual funds = 95

To find the number of clients who own stocks, bonds, and mutual funds (S ∩ B ∩ M), we need to subtract the number of clients who own both pairs of investments and add back the number of clients who own all three:

1. Number of clients who own both stocks and bonds (S ∩ B) = 115
2. Number of clients who own both stocks and mutual funds (S ∩ M) = 100
3. Number of clients who own both bonds and mutual funds (B ∩ M) = 95
4. Number of clients who own stocks, bonds, and mutual funds (S ∩ B ∩ M) = (S ∩ B) + (S ∩ M) + (B ∩ M) - 2(S ∩ B ∩ M)

Plugging in the given values, we get:

Number of clients who own stocks, bonds, and mutual funds (S ∩ B ∩ M) = 115 + 100 + 95 - 2(S ∩ B ∩ M) = 115 + 100 + 95 - 2(0) = 310

Therefore, 310 of Helena's clients own stocks, bonds, and mutual funds.