Question

eyeglassomatic manufactures eyeglasses for different retailers. they test to see how many defective lenses they made in a time period. the following table gives the type of defect and the number of lenses with that defect. assume categories are mutually exclusive.

defect type	frequency
right shaped - small	4692
flaked	1735
wrong axis	1746
chamfer wrong	1425
crazing, cracks	1368
wrong shape	1494
wrong pd	1486
spots and bubbles	1159
wrong height	1897
right shape - big	1870
lost in lab	974
spots/bubbles - intern	972

a) find the probability that a randomly selected defect from the table will be in the category \scratch\ or the category \wrong shape\.
give your answer as a fraction.
give your answer rounded to three decimal places.
b) find the probability that a randomly selected defect is not in the category \scratch\.
given your answer as a fraction.
give your answer rounded to three decimal places.
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Explanation:

Step1: Calculate total number of defects

Sum all frequencies: $5779 + 4692+1735 + 1746+1425+1368+1494+1486+1159+1897+1870+974+972$
$= 26827$

Step2: Calculate number of 'Scratch' or 'Wrong shape' defects

Number of 'Scratch' defects is $5779$, number of 'Wrong shape' defects is $1494$. So total is $5779 + 1494=7273$.

Step3: Calculate probability for part a (fraction)

Probability $P=\frac{7273}{26827}$

Step4: Calculate probability for part a (rounded)

$P=\frac{7273}{26827}\approx 0.271$

Step5: Calculate number of non - 'Scratch' defects

Total defects minus 'Scratch' defects: $26827-5779 = 21048$

Step6: Calculate probability for part b (fraction)

Probability $P=\frac{21048}{26827}$

Step7: Calculate probability for part b (rounded)

$P=\frac{21048}{26827}\approx 0.785$

Answer:

a) $\frac{7273}{26827}$, $0.271$
b) $\frac{21048}{26827}$, $0.785$