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it-is-a-known-that-a-particular-machine-will-make-product-with-a-qualified-rate-of-90-when-it-is-running-well-but-will-do-so-with-a-qualified-rate-of-only-30-when-it-is-not-running-well-The-




Question Number 132439 by liberty last updated on 14/Feb/21
  it is a known that a particular  machine will make product with   a qualified rate of 90% when it is  running well,  but will do so with   a qualified  rate of only 30% when   it is not running well. The  probability that machine is   running well is 75% normally .  Suppose that one day  the first   product made by the machine is   qualified. Find the probabiliy   that the machine is running well at  this time.
$$ \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{known}\:\mathrm{that}\:\mathrm{a}\:\mathrm{particular} \\ $$$$\mathrm{machine}\:\mathrm{will}\:\mathrm{make}\:\mathrm{product}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{90\%}\:\mathrm{when}\:\mathrm{it}\:\mathrm{is} \\ $$$$\mathrm{running}\:\mathrm{well},\:\:\mathrm{but}\:\mathrm{will}\:\mathrm{do}\:\mathrm{so}\:\mathrm{with}\: \\ $$$$\mathrm{a}\:\mathrm{qualified}\:\:\mathrm{rate}\:\mathrm{of}\:\mathrm{only}\:\mathrm{30\%}\:\mathrm{when}\: \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{not}\:\mathrm{running}\:\mathrm{well}.\:\mathrm{The} \\ $$$$\mathrm{probability}\:\mathrm{that}\:\mathrm{machine}\:\mathrm{is}\: \\ $$$$\mathrm{running}\:\mathrm{well}\:\mathrm{is}\:\mathrm{75\%}\:\mathrm{normally}\:. \\ $$$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{one}\:\mathrm{day}\:\:\mathrm{the}\:\mathrm{first}\: \\ $$$$\mathrm{product}\:\mathrm{made}\:\mathrm{by}\:\mathrm{the}\:\mathrm{machine}\:\mathrm{is}\: \\ $$$$\mathrm{qualified}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probabiliy}\: \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{machine}\:\mathrm{is}\:\mathrm{running}\:\mathrm{well}\:\mathrm{at} \\ $$$$\mathrm{this}\:\mathrm{time}.\: \\ $$
Commented by bemath last updated on 14/Feb/21
p= 0.9
$$\mathrm{p}=\:\mathrm{0}.\mathrm{9} \\ $$

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