Consider the following system considering of two switches I and II between two points A and B:

A signal is sent from the point A to point B and is received at B if both the switches I and II are closed. It is assumed that the probabilities of I and II being closed are 0.8 and 0.6 respectively and that P [II is closed | I is closed] = P [II is closed].

Find:

i) The probability that signal is received at B.

ii) The conditional probability that switch I was open, given that the signal was not received at B,

iii) The conditional probability that switch II was open, given that the signal was not received at B.

Given:

• P(I closed)=0.8P(I \text{ closed}) = 0.8

• P(II closed)=0.6P(II \text{ closed}) = 0.6

• P(II closed∣I closed)=P(II closed)=0.6P(II \text{ closed} \mid I \text{ closed}) = P(II \text{ closed}) = 0.6
  This implies the events "I is closed" and "II is closed" are independent.

Let event AA = "signal is received at B", which occurs if both switches are closed.

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