## Related questions with answers

A toy manufacturer buys ball bearings from three different suppliers-50% of her total order comes from supplier 1, 30% from supplier 2, and the rest from supplier 3. Past experience has shown that the quality-control standards of the three suppliers are not all the same. Two percent of the ball bearings produced by supplier 1 are defective, while suppliers 2 and 3 produce defective bearings 3% and 4% of the time, respectively. What proportion of the ball bearings in the toy manufacturer’s inventory are defective?

Solution

VerifiedLet

$A_1$=Supplier 1

$A_2$=Supplier 2

$A_3$=Supplier 3

$B$=defective

Given:

$P(A_1)=50\%=0.50$

$P(A_2)=30\%=0.30$

$P(A_3)=20\%=0.20$

$P(B|A_1)=2\%=0.02$

$P(B|A_2)=3\%=0.03$

$P(B|A_3)=4\%=0.04$

Result theorem of this section:

$P(B)=\sum_{i=1}^n P(B|A_i)P(A_i)$

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