Question

Machines A and B make components, which are then placed on a conveyor belt. Of those made by machine A, 93% are acceptable. Of those made by machine B, 95% are acceptable. Machine A makes 60% of the components and machine B makes the rest. Find the probability that a component selected at random from the conveyor belt is a) made by machine A b) made by machine A and acceptable c) made by machine B and acceptable d) made by machine ad uaeceptable e acceptable f) made by machine A given it is acceptable

Answer 1

	A	B	total
accceptab;e	0.558	0.38	0.938
not acceptable	0.042	0.02	0.062
total	0.6	0.4	1

a) P(machine A) = 0.60  
  
b) P(machine A and acceptable) = 0.60*0.93 = 0.558  
  
c) P(machine B and acceptable) = 0.60*0.95 = 0.38  
  
d) P(machine and unaccepetable) = 0.60*(1-0.95) = 0.02  
  
e) P(acceptable) = 0.558+0.38 = 0.938  
  
f) P(machine A | acceptable) = P(machine A and acceptable)/P(accpetable) = 0.558/0.938= 0.595