Understanding the Problem
The box contains 12 electric lamps, and there are 5 different types of lamps. The goal is to find the expected number of effective lamps when selecting from this collection.
Key Concepts
- Total Lamps: 12
- Different Types: 5
- Effective Lamps: Assume each type has some lamps that are effective.
Calculating Expected Number of Effective Lamps
1. Distribution of Types:
- Since there are 5 different types of lamps, we can assume a uniform distribution where each type has an equal number of lamps.
- Each type could have around 2 or 3 lamps, but for simplicity, we will treat them as equal for our calculations.
2. Probability of Selection:
- When selecting a lamp, the probability of choosing any specific type is 1 out of 5.
3. Expected Value Formula:
- The expected value (E) can be calculated using the formula:
E = (Number of Types) * (Probability of Selecting an Effective Lamp)
- If we assume that each type has an equal chance of being effective, we can estimate the expected number.
Expected Number of Effective Lamps
- If we assume that each lamp selected has a probability of being effective, we can take an average approach.
- For example, if 60% of lamps are effective, then:
- Expected Effective Lamps = 12 * 0.6 = 7.2
Conclusion
The expected number of effective lamps can vary based on the effectiveness ratio of the lamps in the selection. Therefore, a reasonable estimate under uniform conditions would suggest around 7 effective lamps on average.