Certain

A certain product can be produced by two technological procedures. The probability of first-class quality in the first procedure is 0.68, in the second 0.4. All products are stored together. By the first procedure we produce 1.5x more products than by the second.
a) What is the probability that a randomly selected product is first-class?
b) Determine the probability that the first product which was not first-class was produced by the first technological procedure

Final Answer:

a =  0.568
b =  

Step-by-step explanation:

$$\begin{gathered} p_1=0.68 \\ {p}_2=0.4 \\ A:B=1.5 \\ A=1.5\cdot B \\ A+B=1 \\ A-1.5B=0 \\ A+B=1 \\ Row2-Row1\to Row2 \\ 2.5B=1 \\ B=\frac{1}{2.5}=0.4 \\ A=0+1.5B=0+1.5\cdot 0.4=0.6 \\ A=\frac{3}{5}=0.6 \\ B=\frac{2}{5}=0.4 \\ a=p_1\cdot A+p_2\cdot B=0.68\cdot 0.6+0.4\cdot 0.4=0.568 \end{gathered}$$

$b=p_3=1-a=1-0.568=\frac{54}{125}=0.432=$

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