Question

Question #12ac2

Answer 1

`0.93156`

Explanation:

`"2 components in series work if both work, so the reliability"`
`"of the last two branches is 0.95*0.95 = 0.9025."`
`"The last two branches are in parallel. Two components in"`
`"parallel work if at least one works, so the reliability of the two"`
`"last branches together is : 0.9025 + 0.9025 - 0.9025²"`
`"= 0.9025 (2 - 0.9025) = 0.99049"`
`"(because P[A or B]=P[A]+P[B]-P[A and B])"`

`"The first two with reliability 0.9 are also in parallel, so the"`
`"overall reliability of them is : 0.9 + 0.9 - 0.9² = 0.9 (2 - 0.9)"`
`"= 0.99."`

`"So we have three reliabilities in series left so the overall"` `"reliability is : 0.99 * 0.95 * 0.99049 = 0.93156."`