A business man gets a profit of Rs. 2800 with probability 0.5, loss of Rs. 5000 with probability 0.3. and neither profit nor loss with probability 0.2. Find mean of his income.

Answer

To find the mean of the businessman’s income based on the given probabilities and outcomes, we can follow these steps:

### Step 1: Identify the Outcomes and Their Probabilities
We have three outcomes:
1. Profit of Rs. 2800 with a probability of 0.5
2. Loss of Rs. 5000 with a probability of 0.3
3. Neither profit nor loss (which can be considered as Rs. 0) with a probability of 0.2

### Step 2: Calculate the Expected Value for Each Outcome
The expected value (mean) can be calculated by multiplying each outcome by its probability.

1. For the profit:
\[ E_1 = 2800 \times 0.5 = 1400 \]

2. For the loss (note that we consider loss as a negative outcome):
\[ E_2 = -5000 \times 0.3 = -1500 \]

3. For neither profit nor loss:
\[ E_3 = 0 \times 0.2 = 0 \]

### Step 3: Sum Up the Expected Values
Now, we sum up all the expected values to find the overall mean income:
\[ \text{Mean Income} = E_1 + E_2 + E_3 \]
\[ \text{Mean Income} = 1400 - 1500 + 0 = -100 \]

### Final Answer
Thus, the mean of his income is:
\[ \text{Mean Income} = -100 \]