PROBABILITY Eletric Circuit Game ATTENTION If any theorem d

PROBABILITY - Eletric Circuit Game

ATTENTION: If any theorem, definition, lemma or formula is used in the answer, it should be stated and explained why it is been used. Even though the problem may look simple, this is a probability question. Solution needs to be shown STEP by STEP with MATHEMATICAL JUSTIFICATION. Solution wihtout detailed work won\'t be marked. Solution needs to show how and why. FORMAL ANSWER should be applied.

Consider the following portion of an electric circuit with three relays. Current will flow from point a to point b if there is at least one closed path when the relays are activated. The relays may malfunction and not close when activated. Suppose that the relays act independently of one another and close properly when activated with probability 0.9. o-b (a) What is the probability that current flows when the relays are activated? (b) Given that current does not flow when the relays are activated, what is the probability that relay 1 has malfunctioned?

Solution

a) here atleast one relay needs to work. So we find

P(AUB)=P(A)+P(B)-P(A)*P(B)

this is so becaue they are independent.

P(AUB)=0.9+0.9-(0.9*0.9)=0.99

b) For this we find the conditional probability

P(A/B)=P(A and B)/P(B)

P(1 works / current flows)= P(1 works)*P(current flows)/P(current flows)

=0.9*0.99/0.99=0.9009.