GATE Electrical Engineering (EE) 2019 Solved Paper

Question : 55 of 65

Marks: +1, -0

The probability of a resistor being defective is

0.02

. There are 50 such resistors in a circuit. The probability of two or more defective resistors in the circuit (round off to two decimal places) is

Solution:

P = Probability of defective resister

= 0.02

{n}=50 ⇒ λ= {np}=1

Lt X be number of defective Resistors

P(X ≥ 2)=1-P(X<2)

=1-\{ {P}( {X}=0)+ {P}( {X}=1)\}

=1-[\;{ {e}^{-λ} λ^{0}}/{0 !}+\;{ {e}^{-λ} λ^{1}}/{1 !}]

=1\{ {e}^{-1}+ {e}^{-1}\}

=1-\;{2}/{ {e}}

=0.2642

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