using the baysian formula:

P(1&3 working|current flows) = P(1&3 working AND current flows) / P(current flows).

**step 1** find P(1&3 working AND current flows)

this is equal to:

P(1&3&4 working AND 2 not working)

*[this is the case that current flows through 3->4 only)*
+P(1&3&2 working AND 4 not working)

*[this is the case that current flows through 1->2 only)*
+P(1&3&2&4)

*[this is the case that current flows both branches*
=

**Step 2** find P(current flows).

You already worked this out: 0.9639

**Answer**

0.8019/0.9639=0.8319