Question

during the past five years, a stock produced returns of 11 percent, 14 percent, 4 percent, −9 percent, and 5 percent. what is the probability that an investor in this stock will not lose more than 10 percent in any one given year? multiple choice greater than 95 percent greater than 1 percent but less than 2.5 percent greater than .5 but less than 1.0 percent greater than 84 percent but less than 97.5 percent greater than 2.5 percent but less than 16 percent

Explanation:

Step1: Identify relevant years

We have 5 years of returns: 11%, 14%, 4%, -9%, 5%. We need to find how many years have a loss (negative return) not more than 10% (i.e., return ≥ -10%).

Step2: Check each return

• 11%: ≥ -10% (counts)
• 14%: ≥ -10% (counts)
• 4%: ≥ -10% (counts)
• -9%: ≥ -10% (counts, since -9 > -10)
• 5%: ≥ -10% (counts)

All 5 years meet the criteria.

Step3: Calculate probability

Probability = (Number of favorable years) / (Total years) = 5/5 = 1 = 100%? Wait, no—wait, the question is "not lose more than 10%", so losses ≤10% (i.e., returns ≥ -10%). Wait, the only loss here is -9%, which is more than -10%? Wait, no: "not lose more than 10%" means loss ≤10%, so return ≥ -10%. -9% is a loss of 9%, which is ≤10%, so it's acceptable. So all 5 years have returns ≥ -10%. So probability is 5/5 = 1, which is 100%, but the options have "Greater than 95 percent" as an option. Wait, maybe I misread: "not lose more than 10%"—so loss >10% would be return < -10%. How many years have return < -10%? None, because the only negative return is -9%, which is > -10%. So number of years with loss ≤10% (i.e., return ≥ -10%) is 5. So probability is 5/5 = 1, which is 100%, so greater than 95%.

Answer:

A. Greater than 95 percent