[問題]GWD25-6

[magic]

Q6
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
答案是E
為什麼阿??
為什麼不是B呢

[kwtluck]

題目說只要有一個燈泡壞,就算fail
妳選B是任一個燈泡壞的機率, 忽略了兩個同時壞或三個同時壞....
這也都算fail, 所以用1-(沒有任何燈泡壞機率)^10=1-(0.94)^10

[magic]

了解了
謝謝喔

[chris8888]

上面的K大說:妳選B是任一個燈泡壞的機率, 忽略了兩個同時壞或三個同時壞....
這句話有瑕疵
B.(0.06)^10 <== 這是指10 lightbulbs同時壞掉的機率.

事實上, 若用壞掉的角度來思考會很複雜,
1 fails - 9 work
2 fail - 8 work
3 fail - 7 work .... 很難算