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?

Correct result:

p₁ =  72.75 %
p₂ =  24.25 %

Solution:

$$\begin{gathered} q=1-3\mathrm{/}100={\displaystyle \frac{97}{100}}=0.97 \\ {k}_1=75\mathrm{\%}={\displaystyle \frac{75}{100}}=0.75 \\ {k}_2=25\mathrm{\%}={\displaystyle \frac{25}{100}}=0.25 \\ {p}_1=100\cdot q\cdot k_1=100\cdot 0.97\cdot 0.75={\displaystyle \frac{291}{4}}={\displaystyle \frac{291}{4}}\mathrm{\%}=72.75\mathrm{\%} \end{gathered}$$

$p_2=100\cdot q\cdot k_2=100\cdot 0.97\cdot 0.25={\displaystyle \frac{97}{4}}={\displaystyle \frac{97}{4}}\mathrm{\%}=24.25\mathrm{\%}$

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