Question

eyeglassomatic manufactures eyeglasses for different retailers. they test to see how many defective lenses they made in the time period of january 1 to march 31. a sample of 12632 pairs of lenses were inspected. the table below gives the defect and the number of pairs of lenses with that defect. defect type freq scratch 5818 wrong shape 1424 spots and bubbles 970 wrong axis 1866 wrong height 1181 wrong pd 1373 find the probability that a randomly selected a pair of defective lenses will be in the category \spots and bubbles\. give your answer rounded to three decimal places.

Explanation:

Step1: Recall probability formula

The probability $P(A)$ of an event $A$ is given by $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Identify favorable and total outcomes

The number of pairs of lenses with spots and bubbles defect (favorable outcomes) is $n = 970$. The total number of defective lenses (total outcomes) is $N=5818 + 1424+970+1866+1181+1373=12632$.

Step3: Calculate the probability

$P=\frac{970}{12632}\approx 0.077$.

Answer:

$0.077$