If it rains a dealer in rain coats can earn Rs . 500 Rs a day . If it is fair , he can loose Rs.40/- per day . His mean profit if the probability of a fair day is 0.6 is

Options

A. 170
B. 172
C. 274
D. 176

Answer

To find the mean profit of the dealer in raincoats, we will follow these steps:

### Step 1: Define the Earnings
- If it rains, the dealer earns Rs. 500.
- If it is fair (not raining), the dealer loses Rs. 40.

### Step 2: Identify the Probabilities
- The probability of a fair day (not raining) is given as \( P(\text{Fair}) = 0.6 \).
- Therefore, the probability of a rainy day is \( P(\text{Rain}) = 1 - P(\text{Fair}) = 1 - 0.6 = 0.4 \).

### Step 3: Calculate the Mean Profit
The mean profit can be calculated using the formula:
\[ E(X) = P(\text{Rain}) \times \text{Earnings on Rainy Day} + P(\text{Fair}) \times \text{Earnings on Fair Day} \]

Substituting the values:
\[ E(X) = P(\text{Rain}) \times 500 + P(\text{Fair}) \times (-40) \]
\[ E(X) = 0.4 \times 500 + 0.6 \times (-40) \]

### Step 4: Perform the Calculations
1. Calculate the earnings on a rainy day:
\[ 0.4 \times 500 = 200 \]
2. Calculate the earnings on a fair day:
\[ 0.6 \times (-40) = -24 \]

### Step 5: Combine the Results
Now, add the two results together:
\[ E(X) = 200 - 24 = 176 \]

### Conclusion
The mean profit for the dealer in raincoats is Rs. 176.

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