Jt1s tie nust pPobable a party affiliation of the Vöter 8 (2) (16 pts; 4 pts eac
ID: 3305420 • Letter: J
Question
Jt1s tie nust pPobable a party affiliation of the Vöter 8 (2) (16 pts; 4 pts each) t -- Two switches (1) and (2) are connected in series in a line that is connected in paralel to a third switch (3) as shown in the diagram below. These switches work independently when turned on and have the probabilities of working : P(1)=P(2)-8; P(3) = .9 when the switches are turned on (a) Find the probability that the current will flow thru the circuit (b)Find the probability that no current will flow thru the circuit © Find the probability that the current will flow thru both branches of the circuit. (d) Find the probability that the current will flow thru exactly one branch of the circuit DIAGRAMExplanation / Answer
we know that
1)if two switches A and B are connected in series ,probability that current will flow through that branch is P(A)*P(A)
2)if two branches S and T are connected in parallel ,probability that current will flow through that system of branches is 1-(1-P(S))(1-P(T))
Given that
P(switch 1) = 0.8
P(switch 2) = 0.8
P(switch 3) = 0.9
switch 1 and switch 2 are connected in series in branch 1
switch 3 is in branch 2
branch 1 and branch 2 are connected in parallel
a)
Current will flow through the circuit if current flows through either of branches
probabilty that current will flow branch 1 = . 0.8*0.8 = 0.64 i.e P(branch 1) = 0.64
probabilty that current will flow branch 2 = P(switch 3) = 0.9 i.e P(branch 2) = 0.9
Probability that current will flow through circuit = 1- (1-P(branch 1))(1- P(branch 2)) = 1- (1-0.64)(1-0.9) = 0.964
b)
Probability that no current will flow through circuit = 1- Probability that current will flow through circuit
= 1 - 0.964 = 0.036
c)
Probability that current will flow through both the branches = P(branch 1)P(branch 2) = 0.64*0.9 = 0.576
d)
Probability that current will flow through exactly one branch of the circuit = Probability that current will flow through circuit - Probability that current will flow through both the branches = 0.964 - 0.576 = 0.388
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