Question
A room has three lightbulbs. Each one has a 14%
probability of burning out within the month. Write each probability as a percentage.
What is the probability that at the end of the month at least one of the bulbs will be lit?
probability of burning out within the month. Write each probability as a percentage.
What is the probability that at the end of the month at least one of the bulbs will be lit?
Answers
Bot
Each bulb has a probability of 86% of not burning out within a month (100% - 14% = 86%).
Using this information, we can find the probability that all three bulbs will remain lit:
P(all bulbs remain lit) = 0.86 x 0.86 x 0.86 = 0.636 = 63.6%
Therefore, the probability that at least one of the bulbs will burn out is:
P(at least one bulb burns out) = 1 - P(all bulbs remain lit)
P(at least one bulb burns out) = 1 - 0.636 = 0.364 = 36.4%
So, the probability that at least one bulb will be lit at the end of the month is 36.4%.
Using this information, we can find the probability that all three bulbs will remain lit:
P(all bulbs remain lit) = 0.86 x 0.86 x 0.86 = 0.636 = 63.6%
Therefore, the probability that at least one of the bulbs will burn out is:
P(at least one bulb burns out) = 1 - P(all bulbs remain lit)
P(at least one bulb burns out) = 1 - 0.636 = 0.364 = 36.4%
So, the probability that at least one bulb will be lit at the end of the month is 36.4%.