Question

In the given example, there are only three possible weather conditions with their probability (Sunny – 0.2, Cloudy – 0.4, Rainy – 0.4) and the corresponding ice cream sale details given as (Sunny – Rs. 500/-, Cloudy – Rs. 300/-, Rainy – Rs. 100/-). Choose the appropriate expected monetary value

• A. 200
• B. 260
• C. 240
• D. 280

Hint:

To prevent calculation errors, always double-check that the sum of all probabilities equals exactly 1.0: \[ 0.2 + 0.4 + 0.4 = 1.0 \] This ensures a mathematically sound probability distribution.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Expected Monetary Value (EMV) is a statistical concept.
It calculates the average outcome of a decision when the future includes uncertain scenarios with known probabilities.
Key Formula or Approach:
The mathematical formula for Expected Monetary Value is: \[ \text{EMV} = \sum_{i=1}^{n} (P_i \times V_i) \] where:
- $P_i$ is the probability of scenario $i$.
- $V_i$ is the monetary value associated with scenario $i$.

Step 2: Detailed Explanation:
Let us tabulate and calculate the expected value for each weather scenario:
1. Sunny Day:
- Probability ($P_1$) = $0.2$
- Monetary Value ($V_1$) = Rs. $500$
- Contribution $= 0.2 \times 500 = 100$
2. Cloudy Day:
- Probability ($P_2$) = $0.4$
- Monetary Value ($V_2$) = Rs. $300$
- Contribution $= 0.4 \times 300 = 120$
3. Rainy Day:
- Probability ($P_3$) = $0.4$
- Monetary Value ($V_3$) = Rs. $100$
- Contribution $= 0.4 \times 100 = 40$
Sum the individual expected values to calculate the total EMV: \[ \text{EMV} = 100 + 120 + 40 = 260 \]

Step 3: Final Answer:
The expected monetary value for the ice cream sales is Rs. 260.