This is the electric circuit in our problem:
It has 4 parallel connections. There are 8 switches that are independent. Each of the switches is closed in probability of 0.7, and then the electric current can go by the switch. The questions are:
What is the probability that electric current will go from A to B?
It is now known that there are exactly 5 switches open in the 3 bottom branches. What is the probability now that the electric current will flow from A to B?
Now there are exactly 5 switches open in the electric curcuit. What is the probability that the electric current will flow from A to B?
I have trouble building the correct logical intuition to solve the problem. If we are talking about A- the probabilty for switch 1 and switch 2 will both be closed (and then the electric current will go from A to b) is $0.7\times0.7$ and it is equal for the probability that switch 1 and switch 3 will both be close but then the electric current won`t be able to go to B. How do I sepearate between the cases? Meaning between that the electric current will go from A to B and would not go. As you see it has the same probability. When I solve it, how can I promise that only the switches I want will be closed?
Edit- So Q1 we solve with Binomic disturbution. Can I solve Q2 and Q3 by it as well?