Question

A company produces certain types of sophisticated item by three machines. The respective daily production figures are machine A 300 units, Machine B 450 units, and machine C 250 units. Past experience shows that the percentage of defective in the three machines are 0.1,0.2 and 0.7 respectively for machines A B and C. An item is drawn at random from a day's production and is found to be defective. What is the probability that it is not produced by machine C?

Answer 1

Let $E_1,E_2,E_3$ is machine A,B,C

D = defective items

Total production = 300+450+250 = 1000

$P(E_1) = \dfrac{300}{1000}$

$P(E_2) = \dfrac{450}{1000}$

$P(E_3) = \dfrac{250}{1000}$

Now,

$P(\dfrac{D}{E_1}) = 0.001$

$P(\dfrac{D}{E_2}) = 0.002$

$P(\dfrac{D}{E_3}) = 0.007$

Probability = $P(\dfrac{E_3}{D})$ = $\dfrac{\dfrac{250}{1000}\times 0.007}{0.001375}$

= $\dfrac{0.000175}{0.001375}$

= $0.127$

P(not produced by machine C ) = 1 - 0.127

= $0.87$