A purchaser of alarm clocks buys them in lots of size 10. It is his policy to inspect 3 clocks randomly from a lot and to accept the lot only if all 3 are nondefective. If 30 percent of the lots have 4 defective clocks and 70 percent have only 1, what proportion of lots does the purchaser reject?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.5: Interpreting Data
Problem 1C
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A purchaser of alarm clocks buys them in lots of size 10. It is his policy to inspect 3 clocks randomly
from a lot and to accept the lot only if all 3 are nondefective. If 30 percent of the lots have 4 defective
clocks and 70 percent have only 1, what proportion of lots does the purchaser reject?

Expert Solution
Step 1

Define the Events,

A : The lot have 4 defectives

B : The lot have 1 defective

C : The lot purchaser rejects the lot.

Proportion of lots having 4 defectives , P(A) = 30% = 0.3

Proportion of lots having 1 defective, P(B) = 70% = 0.7

By his policy he inspects 3 clocks randomly from a lot and to accept the lot only if all 3 are non defective.

If lot have 4 defectives then the probability that lot is accepted = 4010-43103=1×20120=16

If the lot have 1 defective then the probability that lot is accepted = 1010-13103=84120=0.7

 

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