Max Sandlin is exploring the characteristics of stock market investors. He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage. An investor is selected randomly,and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= _____________.
A) 0.17
B) 0.50
C) 0.80
D) 0.70
E) 0.10

Question

Quizplus · Accepted Answer

From the given information, we know:
P(E) = 0.6 (60% of all investors have a net worth exceeding $1,000,000)
P(O) = 0.2 (20% of all investors use an online brokerage)
P(O ∩ E) = 0.1 (10% of all investors have a net worth exceeding $1,000,000 and use an online brokerage)

We need to find P(O ∩ E') where E' is the complement of event E (i.e., an investor does not have a net worth exceeding $1,000,000). We can use the formula:

P(O ∩ E') = P(O) - P(O ∩ E)

Substituting the given values, we get:

P(O ∩ E') = 0.2 - 0.1 = 0.1

Now we need to find P(O ∩ E' ∪ E), which is the probability that an investor either uses an online brokerage or does not have a net worth exceeding $1,000,000 (or both). We can use the formula:

P(O ∩ E' ∪ E) = P(O ∩ E') + P(E)

Substituting the calculated values, we get:

P(O ∩ E' ∪ E) = 0.1 + 0.6 = 0.7

Therefore, the answer is D) 0.70.

Max Sandlin Is Exploring the Characteristics of Stock Market Investors ∪\cup∪

Max Sandlin Is Exploring the Characteristics of Stock Market Investors $\cup$