Probability of bulb malfunction

You used the correct formula for binomial probability, and your answer is the probability that none of the bulbs in an 8-pack will fail on the first use. The given answer is much larger than 1, which is impossible for a probability.
  • #1
tzx9633

Homework Statement


consider 8 packs of bulb and let x be the number of bulbs in a pack that 'fail' the first time they are used . If 0.02 of all bulbs of this type fail on their first use and each 8-pack is consider random sample , what is the probability that anyone 8-pack has no bulb fail on the first use ?

Homework Equations

The Attempt at a Solution


I use binomial probability to solve this . But my ans didnt match the ans given
My ans :
(8c0)(0.02^0)(0.98^8) = 0.8507 , the ans given = 0.3012
 
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  • #2
tzx9633 said:

Homework Statement


consider 8 packs of bulb and let x be the number of bulbs in a pack that 'fail' the first time they are used . If 0.02 of all bulbs of this type fail on their first use and each 8-pack is consider random sample , what is the probability that anyone 8-pack has no bulb fail on the first use ?

Homework Equations

The Attempt at a Solution


I use binomial probability to solve this . But my ans didnt match the ans given
My ans :
(8c0)(0.02^0)(0.98^8) = 0.8507 , the ans given = 0.3012

Your answer is correct; the "given" answer makes no sense at all in this problem.
 
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1. What is the probability of a bulb malfunctioning?

The probability of a bulb malfunctioning is dependent on various factors such as the quality of the bulb, usage patterns, and environmental conditions. However, on average, the probability of a bulb malfunctioning is estimated to be around 5-10%.

2. How do you calculate the probability of a bulb malfunctioning?

The probability of a bulb malfunctioning can be calculated by dividing the number of malfunctioning bulbs by the total number of bulbs in a given sample. This calculation can then be expressed as a percentage to determine the probability.

3. Can the probability of a bulb malfunctioning be reduced?

Yes, the probability of a bulb malfunctioning can be reduced by using high-quality bulbs, following proper usage and maintenance guidelines, and controlling environmental factors such as temperature and humidity.

4. Is the probability of a bulb malfunctioning the same for all types of bulbs?

No, the probability of a bulb malfunctioning can vary for different types of bulbs. For example, LED bulbs have a lower probability of malfunctioning compared to incandescent bulbs.

5. How does the probability of a bulb malfunctioning affect the overall reliability of a lighting system?

The probability of a bulb malfunctioning can significantly impact the reliability of a lighting system. A higher probability of malfunctioning can lead to more frequent replacements and potential downtime, which can be costly for businesses. Therefore, it is essential to consider the probability of bulb malfunctioning when designing a lighting system for optimal reliability.

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