Calculating Probability for Light Bulb Working

What is the probability that all 10 light bulbs work?

Given that each light bulb's working condition is independent and the probability of each light bulb working is 0.6, what is the likelihood that all 10 light bulbs will work?

Answer:

The probability of all 10 light bulbs working is 0.006.

In this scenario, we have 10 light bulbs in a classroom, and the probability of each individual light bulb working is 0.6. It is also stated that each light bulb works independently of the others, meaning the working condition of one light bulb does not affect the others.

To calculate the probability of all 10 light bulbs working, we need to consider the probability of each individual light bulb working and then multiply them together. Since each event is independent, we can simply multiply the individual probabilities to get the overall probability.

The calculation would be as follows:

Probability = 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6 x 0.6

Probability = 0.0060466 (approximately 0.006)

Therefore, the likelihood of all 10 light bulbs working is approximately 0.006 or 0.6%.