The fair price of a raffle ticket is equivalent to the expected value (EV) of the outcomes. To compute the EV, we multiply each prize by its probability of occurrence and sum up these values.

Given:

• First prize: P15,000, probability = 0.002% = 0.00002
• Second prize: P12,000, probability = 0.0015% = 0.000015

The formula for expected value is:

$EV = (Prize_1 \times Probability_1) + (Prize_2 \times Probability_2)$

Calculations:

1. Contribution of the first prize:

$15,000 \times 0.00002 = 0.3 \, \text{(P)}$

2. Contribution of the second prize:

$12,000 \times 0.000015 = 0.18 \, \text{(P)}$

3. Total EV:

$EV = 0.3 + 0.18 = 0.48 \, \text{(P)}$

Final Answer:

The fair price of the raffle ticket is P0.48.

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Would you like further details or any clarifications? Here are some related questions:

1. What is the expected value concept in probability, and why is it important?
2. How do probabilities in percentages translate into decimal form?
3. What happens to the fair price if additional prizes are added?
4. How do we account for the cost of the raffle ticket when calculating its value?
5. Can EV guarantee that you will make a profit when buying a ticket?

Tip: To convert probabilities from percentages to decimals, divide the percentage by 100. For example, $0.002\% \to 0.002 \div 100 = 0.00002$.