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	4595
flaked	1217
wrong axis	1754
chamfer wrong	1350
crazing, cracks	1574
wrong shape	1266
wrong pd	1761
spots and bubbles	1748
wrong height	1301
right shape - big	1541
lost in lab	989
spots/bubbles - intern	984

a) find the probability that a randomly selected defect from the table will be in the categor \wrong shape\ or the category \scratch\.
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 \wrong shape\.
given your answer as a fraction.
give your answer rounded to three decimal places.
question help: video 1 video 2 message instructor

Explanation:

Step1: Calculate total number of defects

Sum up all frequencies.
$5863 + 4595+1217 + 1754+1350+1574+1266+1761+1748+1301+1541+989+984$
$= 25943$

Step2: Calculate number of "Wrong shape" and "Scratch" defects

Add frequencies of "Wrong shape" and "Scratch".
$1266+5863 = 7129$

Step3: Calculate probability for part a

Probability is number of favorable outcomes over total outcomes.
Fraction: $\frac{7129}{25943}$
Rounded to three - decimal places: $\frac{7129}{25943}\approx0.275$

Step4: Calculate probability for part b

Probability of not "Wrong shape" is 1 minus probability of "Wrong shape".
Number of "Wrong shape" defects is 1266.
Probability of "Wrong shape" is $\frac{1266}{25943}$.
Probability of not "Wrong shape":
Fraction: $1-\frac{1266}{25943}=\frac{25943 - 1266}{25943}=\frac{24677}{25943}$
Rounded to three - decimal places: $\frac{24677}{25943}\approx0.951$

Answer:

a) $\frac{7129}{25943}$, $0.275$
b) $\frac{24677}{25943}$, $0.951$