There are five components. The components act independently, with component i working with probability pi

$,$

i

$=$

$1$

$,$

$2$

$,$

$3$

$,$

$4$

$,$

$5$

$.$

$$Component

$1$

$$links points A and C

$,$

$$component

$2$

$$

$$A and D

$,$

$$component

$3$

$$

$$C and D

$,$

component

$4$

$$

$$C and B

$,$

$$component

$5$

$$

$$D and B

$.$

$$The system is said to work if a signal originating at point

A can reach point B

$,$

$$where it can pass through a component only if that component is working. What is the

probability that the system works?