Question

in a bolt factory machine A B and C manufacture respectively 25% 35% and 40% of the total bolts of their the outputs 5,4 and 2 are respectively defective A bolt is drawn at random from the.
product what is the probability that the random ball is defective

Answer 1

Answer:

28/69

Step-by-step explanation:

Let S be the probability of defective bolt and T1, T2 and T3 be the event of drawing a bolt produced by the Machines A, B and C respectively. Then  

P(T1) = 25/100, P(T2) = 35/100, P(T3) = 40/100, P(S/T1) = 5/100, P(S/T2) = 4/100, P(S/T3) = 2/100.  

Therefore, P(T2/S) = [P(T2).P(S/T2)]/[P(T1).P(S/T1) + P(T2).P(S/T2) + P(T3).P(S/T3)]  

= [(35/100) x (4/100)] / [(25/100) x (5/100) + (35/100) x (4/100)  

+ (40/100) x (2/100)]  

= [35×4] / [25×5 + 35×4 + 40×2]  

= 140 / (125 + 140 + 80)  

= 140/345  

= 28/69