Question

A bolt manufacturing company has three machines A,B,C which produce 25%, 35% and 40% of the bolts respectively. It is known that the percentage of the defective bolts produced by A,B,C are respectively 4%, 2% and 2.5%. A bolt is drawn at random from the lot and is found to be defective what is the probability that the defective bolt came from the machine A

Answer 1

Answer:

P(defective bolt from A)= $\frac{2}{5}$

Step-by-step explanation:

Let,

E1: the event that bolt is produced by machine A.  

E2: the event that bolt is produced by machine B.

E3: the event that bolt is produced by machine C.

A: the event that bolt chosen is found to be defective

Given:

P(E1)=25/100, P(E2)=35/100, P(E3)=40/100

P(A|E1)=4/100, P(A|E2)=2/100, P(A|E3)=2.5/100

To find: P(defective bolt from machine A)

$P(E3|A)=\frac{P(E1)*P(A|E1)}{P(E1)*P(A|E1)+P(E2)*P(A|E2)+P(E3)*P(A|E3)}$

$P(E3|A)=\frac{25/100*4/100}{25/100*4/100+25/100*2/100+40/100*2.5/100}$

$P(E3|A)=\frac{100}{100+50+100}=\frac{100}{250}=\frac{2}{5}$

Answer 2

Answer:

Answer:

P(defective bolt from A)= \frac{2}{5}

5

2

Step-by-step explanation:

Let,

E1: the event that bolt is produced by machine A.

E2: the event that bolt is produced by machine B.

E3: the event that bolt is produced by machine C.

A: the event that bolt chosen is found to be defective

Given:

P(E1)=25/100, P(E2)=35/100, P(E3)=40/100

P(A|E1)=4/100, P(A|E2)=2/100, P(A|E3)=2.5/100

To find: P(defective bolt from machine A)

P(E3|A)=\frac{P(E1)*P(A|E1)}{P(E1)*P(A|E1)+P(E2)*P(A|E2)+P(E3)*P(A|E3)}P(E3∣A)=

P(E1)∗P(A∣E1)+P(E2)∗P(A∣E2)+P(E3)∗P(A∣E3)

P(E1)∗P(A∣E1)

P(E3|A)=\frac{25/100*4/100}{25/100*4/100+25/100*2/100+40/100*2.5/100}P(E3∣A)=

25/100∗4/100+25/100∗2/100+40/100∗2.5/100

25/100∗4/100

P(E3|A)=\frac{100}{100+50+100}=\frac{100}{250}=\frac{2}{5}P(E3∣A)=

100+50+100

100

=

250

100

=

5

2