Answer :
To find the expected value and assess the risk of an investment worth [tex]$50,000 with different probabilities of returns, we follow these steps:
### Step 1: Understanding the Probability and Returns
- There is a 30% chance (0.30 probability) that the investment ends up being worth $[/tex]40,000.
- There is a 50% chance (0.50 probability) that the investment ends up being worth [tex]$50,100. - There is a 20% chance (0.20 probability) that the investment ends up being worth $[/tex]65,000.
### Step 2: Calculating the Expected Value
The expected value (EV) is calculated using the formula:
[tex]\[ EV = (Probability_1 \times Return_1) + (Probability_2 \times Return_2) + (Probability_3 \times Return_3) \][/tex]
Plugging in the given values:
[tex]\[ EV = (0.30 \times 40000) + (0.50 \times 50100) + (0.20 \times 65000) \][/tex]
[tex]\[ EV = 12000 + 25050 + 13000 \][/tex]
[tex]\[ EV = 50050 \][/tex]
Therefore, the expected value of the investment is [tex]$50,050. ### Step 3: Assessing the Risk of the Investment To determine if the investment is risky, we consider the probability of making a significant return, which we define as earning an amount greater than the initial investment of $[/tex]50,000.
We need to check the probabilities of returns exceeding [tex]$50,000: - The investment amount of $[/tex]50,100 exceeds [tex]$50,000, with a probability of 50%. - The investment amount of $[/tex]65,000 exceeds [tex]$50,000, with a probability of 20%. Adding these probabilities gives: \[ 50\% + 20\% = 70\% \] Therefore, the investment has a 70% chance of making a significant return (greater than $[/tex]50,000).
### Conclusion
The expected value of the investment is [tex]$50,050. The investment is not considered risky because it has a 70% chance of making a significant return. These are the values needed: - The expected value of the investment is $[/tex]50,050.
- The investment has a 70% chance of making a significant return.
- There is a 50% chance (0.50 probability) that the investment ends up being worth [tex]$50,100. - There is a 20% chance (0.20 probability) that the investment ends up being worth $[/tex]65,000.
### Step 2: Calculating the Expected Value
The expected value (EV) is calculated using the formula:
[tex]\[ EV = (Probability_1 \times Return_1) + (Probability_2 \times Return_2) + (Probability_3 \times Return_3) \][/tex]
Plugging in the given values:
[tex]\[ EV = (0.30 \times 40000) + (0.50 \times 50100) + (0.20 \times 65000) \][/tex]
[tex]\[ EV = 12000 + 25050 + 13000 \][/tex]
[tex]\[ EV = 50050 \][/tex]
Therefore, the expected value of the investment is [tex]$50,050. ### Step 3: Assessing the Risk of the Investment To determine if the investment is risky, we consider the probability of making a significant return, which we define as earning an amount greater than the initial investment of $[/tex]50,000.
We need to check the probabilities of returns exceeding [tex]$50,000: - The investment amount of $[/tex]50,100 exceeds [tex]$50,000, with a probability of 50%. - The investment amount of $[/tex]65,000 exceeds [tex]$50,000, with a probability of 20%. Adding these probabilities gives: \[ 50\% + 20\% = 70\% \] Therefore, the investment has a 70% chance of making a significant return (greater than $[/tex]50,000).
### Conclusion
The expected value of the investment is [tex]$50,050. The investment is not considered risky because it has a 70% chance of making a significant return. These are the values needed: - The expected value of the investment is $[/tex]50,050.
- The investment has a 70% chance of making a significant return.
