Needgmat wrote:A string of 10 lightbulbs is wired in such a way that if any individual lightbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during time period T is 0.06, what is the probability that the string of lightbulbs will fail during time period T?
A) 0.06
B) (0.06)^10
C) 1-(0.06)^10
D) (0.94)^10
E) 1-(0.94)^10
OAE
We are given that, in a string of light bulbs, if any individual light bulb fails, the entire string fails. We need to find the probability that the string of light bulbs will fail during time period T. In other words we need to determine the probability that
at least one light bulb fails.
It is instrumental in this problem to find the probability of the complement of the event of interest. If we find the probability that no light bulbs fail (i.e. that the string works properly), and then subtract that probability from 1, then we can easily find the probability that at least one light bulb fails.
Since P(at least one light bulb failing) + P(none of the 10 lightbulbs failing) = 1
P(at least one light bulb failing) = 1 - P(none of the 10 lightbulbs failing)
Thus, it's easiest to determine 1 - P(none of the 10 lightbulbs failing).
Since the probability that a light bulb will fail is 0.06 is, the probability that a light bulb won't fail is 1 - 0.06 = 0.94.
Thus, the probability that none of the 10 light bulbs fail is:
0.94 x 0.94 x 0.94 x 0.94 x 0.94 x 0.94 x 0.94 x 0.94 x 0.94 x 0.94
(0.94)^10
P(at least one light bulb failing) = 1 - (0.94)^10
Answer:
E
