Quality class

The probability that a product is of 1st, 2nd or 3rd quality class is 0.5, 0.3 and 0.2. The probability that products in these quality classes pass acceptance inspection at the customer is respectively 0.9, 0.7 and 0.2.
a) What is the probability that a randomly selected product passes acceptance inspection?
b) The product passed acceptance inspection. What is the probability that it is a product of the 2nd quality class?

Final Answer:

p₁ =  0.7
p₂ =  0.4286

Step-by-step explanation:

$p_1=0.5\cdot 0.9+0.3\cdot 0.7+0.2\cdot 0.2=0.7$

$p_2=\frac{0.3}{p_1}=\frac{0.3}{0.7}=\frac{3}{7}=0.4286$

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