Question

chapter 3: 3.2 independent and mutually exclusive events homework score: 9/15 answered: 10/14 question 10 score on last try: 0 of 1 pts. see details for more. next question get a similar question with one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. the abc electronics company has just manufactured 1650 write - rewrite cds, and 90 are defective. if 6 of these cds are randomly selected for testing, what is the probability that the entire batch will be accepted? rounded to four decimal place accuracy. 0.6040 × 0.7139

Explanation:

Step1: Calculate non - defective CDs

The number of non - defective CDs is $1650 - 90=1560$.

Step2: Use combination formula for probability

The total number of ways to select 6 CDs out of 1650 is $C(1650,6)=\frac{1650!}{6!(1650 - 6)!}$.
The number of ways to select 6 non - defective CDs out of 1560 is $C(1560,6)=\frac{1560!}{6!(1560 - 6)!}$.
The probability $P$ that the entire batch is accepted (i.e., all 6 selected CDs are non - defective) is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[P=\frac{C(1560,6)}{C(1650,6)}=\frac{\frac{1560!}{6!(1560 - 6)!}}{\frac{1650!}{6!(1650 - 6)!}}=\frac{1560!×(1650 - 6)!}{(1560 - 6)!×1650!}\]
\[P=\frac{1560\times1559\times1558\times1557\times1556\times1555}{1650\times1649\times1648\times1647\times1646\times1645}\approx0.7139\]

Answer:

$0.7139$