tonytran14896 wrote:
A string of 10 lightbulbs is wired in such a way that if any individual lighbulb fails, the entire string fails. If for each individual lightbulb the probability of failing during a certain time period is 0.05, what is the probability that the string of lightbulbs will NOT fail during said time period?
a. 0.05
b. (0.05)^10
c. 1 - (0.05)^10
d. (0.95)^10
e. 1 - (0.95)^10
Think about it: When will the string of lightbulbs not fail? Only when all lightbulbs stay alive simultaneously.
P (a lightbulb will stay alive) = 1 - 0.05 = 0.95
So probability that all lightbulbs stay live simultaneously \(= 0.95 * 0.95 * 0.95.....0.95 = (0.95)^{10}\)
(0.95s will be multiplied because it is an "and" situation. You need the first "and" the second "and" the third etc to stay alive)
Answer (D)
asking this out of curiosity .what will be the question if the answer would be c .
my thinking is a bit weird please forgive me.