A room has three lightbulbs. Each one has a 9%
probability of burning out within the month. Write each probability as a percentage.
What is the probability that all three will burn out within the month?
Each lightbulb has a 9% probability of burning out within the month. To determine the probability that all three will burn out within the month, we need to multiply the probabilities of each individual lightbulb burning out. We use the multiplication rule of probability which states that the probability of two (or more) independent events occurring together equals the product of their individual probabilities:
P(all three burn out) = P(first burns out) x P(second burns out) x P(third burns out)
P(all three burn out) = 0.09 x 0.09 x 0.09
P(all three burn out) = 0.000729
Therefore, the probability that all three lightbulbs will burn out within the month is 0.000729, or approximately 0.073% (0.0729 x 100).