a section of an electrical circuit has two... 1. A section of an electrical circ

Question

a section of an electrical circuit has two... 1. A section of an electrical circuit has two relays, numbered 1 and 2, operating in parallel. The current will flow when a switch is thrown if either one or both of the relays close. The probability of a relay closing properly is 0.8 for each relay. We assume that the relays operate independently. Let Ei denote the event that relay i closes properly when the switch is thrown. Define the random variable X to be the number of relays that close properly when the switch is thrown. What values does X take ? Find P(X = 0), P(X = 1) and P(X = 2). Z.

Explanation / Answer

Here we use binomial distin=bution to find this probability

P=0.8 3 Probability of a ralay closing properly

n=2 # only two relays

What are possible values of X

>> 0 ,1,2

binomial distribution formula

P(X=x) = nCx * Px * (1-P)n-x

P(X=0)=  2C0* (0.8)0 * (0.2)2

= 1 * 1 * 0.04

= 0.04

P(X=1)=  2C1* (0.8)1 * (0.2)1

= 2 * 0.8 *0.2

= 0.32

P(X=2)=  2C2* (0.8)2 * (0.2)0

= 1 *0.64*1

= 0.64

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