Question

A bicycle factory runs two assembly​ lines, A and B. 97​% of line​ A's products pass inspection and 94​% of line​ B's products pass inspection. 40​% of the​ factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the​ factory's bikes passedpassed inspection and came off assembly line B.

Answer 1

The probability that one of the​ factory's bikes passed inspection and came off assembly line B is 0.564.

Explanation:

Given : A bicycle factory runs two assembly​ lines, A and B. 97​% of line​ A's products pass inspection and 94​% of line​ B's products pass inspection. 40​% of the​ factory's bikes come off assembly line B and the rest come off line A.

To find : The probability that one of the​ factory's bikes passed inspection and came off assembly line B ?

Solution :

The probability of line​ B's is P(B)= 40%=0.4

The probability of line​ A's is P(A)=100-40= 60%=0.6

Let E be the passes inspection.

The probability of line​ A's products pass inspection is P(E/A)=97%=0.97

The probability of line​ B's products pass inspection is P(E/B)=94%=0.94

The probability that one of the​ factory's bikes passed inspection and came off assembly line B is
`P(B\cap E)`

`P(B\cap E)=P(B)\cdot P(E/B)`

`P(B\cap E)=(0.6)(0.94)`

`P(B\cap E)=0.564`

Therefore, The probability that one of the​ factory's bikes passed inspection and came off assembly line B is 0.564.