A company makes electric motors. The probability an electric motor is defective is 0.04. What is the probability that a sample of 200 electric motors will contain
exactly 4 defective motors?
Step-by-step explanation:
[tex]Probability \: of \: defective \: electric \: motor \: \\ q = 0.04 \\ \\ Probability \: of \: working \: electric \: motor \\ p = 1-q \\ =1-0.04 \\ =0.96 \\ \\ n \: = total \: =200 \\ \\ Exactly \: defective \: motors \: is \: 4 \\ \\ Using \: binomial \: theorem \implies \\ \\ \\ {(x + a)}^{n} \\ \\ \implies \: \binom{200}{4} (0.96)^{195} (0.04)^4 \\ \\ Simplify \\ \\ Probablity(X=x=195) = \binom{200}{4} \times (0.96)^{195} \times (0.04)^4[/tex]
[tex] Note :- \binom{n}{r} = nC_r [/tex]
