# A Company has two plants to manufacture cycles. The first plant manufactures 60% of thecycles and the second plant manufactures 40%. 80% of the cycles of the first plant are ratedof standard quality and 90% of the cycles of the second plant are rated of standard quality. Acycle is picked up at random and it is found to be of standard quality. Find the probabilitythat it comes from the second plant.

yaswanth
36 Points
7 years ago
2/5.9/10+3/5.4/5
=18/42
=3/7

ARUN KAUSHIK N R
18 Points
7 years ago
let f be event that the cycle is from first plant.
let s be event that the cycle is from second plant.
let g be event that the cycle is  of standard quality.
from sum,           P(f)=0.6,                 P(s)=0.4,
P(g/f)=0.8,              P(g/s)=0.9
required probability=P(s/g)
=P(g/s) .P(s) / { P(g/f).P(f) +P(g/s) .P(s)} (by bayes theorem)
= 0.4*0.9 / {0.6*0.8 + 0.4*0.9}
= 0.36/0.84
= 3/7
= 0.42857

ARUN KAUSHIK N R
18 Points
7 years ago
let f be event that the cycle is from first plant.
let s be event that the cycle is from second plant.
let g be event that the cycle is  of standard quality.
from sum,           P(f)=0.6,                 P(s)=0.4,
P(g/f)=0.8,              P(g/s)=0.9
required probability=P(s/g)
=P(g/s) .P(s) / { P(g/f).P(f) +P(g/s) .P(s)} (by bayes theorem)
= 0.4*0.9 / {0.6*0.8 + 0.4*0.9}
= 0.36/0.84
= 3/7
= 0.42857

ARUN KAUSHIK N R
18 Points
7 years ago
let f be event that the cycle is from first plant.
let s be event that the cycle is from second plant.
let g be event that the cycle is  of standard quality.
from sum,           P(f)=0.6,                 P(s)=0.4,
P(g/f)=0.8,              P(g/s)=0.9
required probability=P(s/g)
=P(g/s) .P(s) / { P(g/f).P(f) +P(g/s) .P(s)} (by bayes theorem)
= 0.4*0.9 / {0.6*0.8 + 0.4*0.9}
= 0.36/0.84
= 3/7
= 0.42857

Aryakanya Amin
23 Points
7 years ago
A= standered quality cycles
P(E1) = cycles frm 1st plant= 60/100
P(E2) = cycles frm 2nd plant= 40/100
P(A/E1) = 80/100
P(A/E2) = 90/100

P(E2/A)= P(E2)*P(A/E2)
P(E1)*P(A/E1)
=40/100*90/100
40/100*90/100 + 60/100*80/100
=  36/100
36/100 +48/100
= 36/84 = 6/14  = 3/7 :)