Problem 26E
Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

Only contacts 
Only glasses 
Both 
Neither 
Total 
Male 
64 
841 
177 
456 
1538 
Female 
189 
427 
368 
681 
1665 
Total 
253 
1268 
545 
1137 
3203 
(a) The person wears only contacts or only glasses.
(b) The person is male or wears both contacts and glasses.
(c) The person is female or wears neither contacts nor glasses.
(d) The person is male or does not wear glasses.
Solution :
Step 1 of 4:
Given the results of a survey that asked 3203 people whether they wore contacts or glasses.
Then the table is given below,
Only contacts 
Only glasses 
Both 
Neither 
Total 

Male 
64 
841 
177 
456 
1538 
Female 
189 
427 
368 
681 
1665 
Total 
253 
1268 
545 
1137 
3203 
a). We need to find the probability that the person wears only contacts or only glasses.
Then the probability that the person wears only contacts or only glasses is
P(only contacts or only glasses) = P(only contacts)+P(only glasses)
P(only contacts or only glasses) =
P(only contacts or only glasses) =
P(only contacts or only glasses) = 0.2491
Therefore, the probability that the person wears only contacts or only glasses is 0.2491.