热心人帮解一道数学题（概率）

cheryong

本人对概率题一塌糊涂，求助热心人，能否给一个详解过程从而帮助把此类题融会贯通。

另：" ^ " (请问这个符号是什么意思，谢谢)

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 id 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

nocturnetian

at least one lightbulb fails, then the string of lightbulb will fail.

so we shuold rule out the probability that no lightbulb fails. for

each individual lightbulb the probability of failing during

time period T is 0.06,  so, the probability of unfailing is (1-0.06), and the probability of unfailing for 10 lightbulbs is (1-0.06)^10, then the probability of failing for at least one lightbulb  is  1-(1-0.06)^10.