If the probability that each switch is closed is p, then find the probability of current flowing through AB [DCE 2005]
A) \[{{p}^{2}}+p\]
B) \[{{p}^{3}}+p-1\]
C) \[{{p}^{3}}+p\]
D) \[{{p}^{2}}+p+1\]
Correct Answer: A
Solution :
Current in the upper part will flow only if both the switches a and b are closed \[\therefore \] Their probability = p.p. = \[{{p}^{2}}\] Now current will flow in lower part of c, if c is closed, its probability is p. Thus current will flow from A to B if current flows either in upper part or flow in lower part. \ Required probability =\[{{p}^{2}}+p\].
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