1. ## Probability problem

A local telephone call goes through three independent sets of equipment, the outgoing telephone, the automatic exchange, and the receiving telephone. If the probability of failure on the outgoing phone is 0.05, the probability on the exchange is 0.01, and the probability on the receiving phone is 0.04, find the probability that if a call is not connected it is at least partly the fault of the exchange.

I have attached my tree diagram.
I found the probability of all the points where the exchange is faulty
$\displaystyle 0.05\times0.01\times0.04=0.00002$
$\displaystyle 0.05\times0.01\times0.96=0.00048$
$\displaystyle 0.95\times0.01\times0.04=0.00038$
$\displaystyle 0.95\times0.01\times0.96=0.00912$
The total then is 0.01, but the answer is supposed to be 0.1030.
Where have i gone wrong?

2. You calculated all the cases where the exchange was at fault.

You didn't use the fact that the call didn't go through - in other words you need to omit the case where all 3 parts are working from your entire space. That should bump up your calculated value.