# The manufacturer

The manufacturer found that 3% of the plates produced had a malfunction. Of the compliant, 75% are first and 25% second. What is the probability of producing first and second class plates?

Result

p1 =  72.75 %
p2 =  24.25 %

#### Solution:

$q=1-3/100=\dfrac{ 97 }{ 100 }=0.97 \ \\ k_{1}=75 \%=\dfrac{ 75 }{ 100 }=0.75 \ \\ k_{2}=25 \%=\dfrac{ 25 }{ 100 }=0.25 \ \\ \ \\ p_{1}=100 \cdot \ q \cdot \ k_{1}=100 \cdot \ 0.97 \cdot \ 0.75=\dfrac{ 291 }{ 4 }=72.75=72.75 \%$
$p_{2}=100 \cdot \ q \cdot \ k_{2}=100 \cdot \ 0.97 \cdot \ 0.25=\dfrac{ 97 }{ 4 }=24.25=24.25 \%$

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