an investor estimates that there is a 1 in 10 chance that a stock purchase will lose 20% of its value,2 in 10 chance that it will break even,4 in 10 chance that it will gain 15% and 3 in 10 chance that it willgain 30%.whats the expected return

0.065

To calculate the expected return, we need to multiply each possible outcome by its corresponding probability and then sum up the results.

Given the probabilities and their corresponding outcomes:
- Probability of losing 20%: 1 in 10 (1/10)
- Probability of breaking even: 2 in 10 (2/10)
- Probability of gaining 15%: 4 in 10 (4/10)
- Probability of gaining 30%: 3 in 10 (3/10)

Now, let's calculate the expected return step by step:

1. Calculate the loss outcome:
Probability of losing 20% × Return on Loss = (1/10) × (-20%) = -2%

2. Calculate the break-even outcome:
Probability of breaking even × Return on Break-even = (2/10) × 0% = 0%

3. Calculate the gain of 15% outcome:
Probability of gaining 15% × Return on Gain of 15% = (4/10) × 15% = 6%

4. Calculate the gain of 30% outcome:
Probability of gaining 30% × Return on Gain of 30% = (3/10) × 30% = 9%

Now, let's sum up the results:

Expected Return = (-2%) + 0% + 6% + 9% = 13%

Therefore, the expected return of this stock purchase is 13%.