It is estimated that 28% of all adults in the United States invest in stocks and that 86% of U.S. adults have investments in fixed income instruments (savings accounts, bonds, etc.). It is also estimated that 25% of U.S. adults have investments in both stocks and fixed income instruments.What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to 2 decimal places.

To solve this problem, we need to find the probability that a randomly chosen stock investor also invests in fixed income instruments. We can use the formula for conditional probability:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Where:
- \( P(A|B) \) is the probability that event \( A \) occurs given that event \( B \) has occurred.
- \( P(A \cap B) \) is the probability that both events \( A \) and \( B \) occur.
- \( P(B) \) is the probability that event \( B \) occurs.

In this case:
- Let \( A \) be the event that an adult invests in fixed income instruments.
- Let \( B \) be the event that an adult invests in stocks.

Given:
- \( P(A) = 0.86 \) (86% of adults have investments in fixed income instruments)
- \( P(B) = 0.28 \) (28% of adults invest in stocks)
- \( P(A \cap B) = 0.25 \) (25% of adults invest in both stocks and fixed income instruments)

We want to find \( P(A|B) \), the probability that a stock investor also invests in fixed income instruments:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.25}{0.28} \approx 0.8929
\]

Rounding the result to two decimal places:

\[
P(A|B) \approx 0.89
\]

Thus, the probability that a randomly chosen stock investor also invests in fixed income instruments is approximately 0.89.

---

Would you like further explanation on any part of the solution? If you have more questions or need additional assistance, feel free to ask!

Here are some related questions that might interest you:

1. What is the probability that a randomly chosen person invests in either stocks or fixed income instruments?
2. How do we calculate the probability of a person investing in neither stocks nor fixed income instruments?
3. If the total adult population is 250 million, how many adults invest in both stocks and fixed income instruments?
4. What is the probability that a randomly chosen person who invests in fixed income instruments also invests in stocks?
5. How would the probability change if only 20% of adults invest in both stocks and fixed income instruments?
6. What does the complement rule tell us about these probabilities?
7. How would we use a Venn diagram to visualize this problem?
8. What is the probability that a randomly chosen person invests only in fixed income instruments?

**Tip:** Conditional probability helps us determine how likely an event is to happen given that another event has already occurred, which can be especially useful in finance and investment analysis.

Learn how to calculate the probability that a randomly chosen stock investor also invests in fixed income instruments using conditional probability. This problem involves understanding probabilities in finance and requires knowledge of conditional probability formulas and set theory concepts. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation