A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study. Suppose two adults are selected from the population independently and at random.What is the probability that both were judged to need eyeglasses and neither was using them for reading?
A)0.36
B)0.1296
C)0.0324
D)0.9216
E)0.18

Question

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study.  Suppose two adults are selected from the population independently and at random.What is the probability that both were judged to need eyeglasses and neither was using them for reading?
A)0.36 
B)0.1296 
C)0.0324 
D)0.9216 
E)0.18

Quizplus · Accepted Answer

Let A be the event that an adult is judged to need glasses and B be the event that an adult is not using glasses.

From the table, we know that:

P(A) = 0.5 (50% of adults were judged to need glasses)

P(B|A) = 0.4 (40% of adults judged to need glasses were not using them)

P(B|A') = 0.95 (95% of adults judged not to need glasses were not using them)

To find the probability that both adults meet the given criteria, we need to find the probability of the intersection of the two events:

P(A and B) = P(A) * P(B|A) * P(B|A')

= 0.5 * 0.4 * 0.95

= 0.19

Therefore, the probability that both adults were judged to need eyeglasses and neither was using them for reading is 0.19 or 0.0324 when rounded to four decimal places.

The correct answer is C.

A Study Was Conducted in a Large Population of Adults