(d) The person is female or not frequently involved in 26....

(d) The person is female or not frequently involved in 26. 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.

Transcript

00:02 In your question, you're given the table of information about males and females, whether they wear contacts, glasses, both, or neither.

00:09 We're asked to find the following four probabilities, which are all or probabilities, which means there are a combination of groups.

00:19 Part a, we're looking for the probability of only contacts or only glasses.

00:24 Now, for those two groups, there's no overlap, where we would have overlap.

00:30 You can't have it if they're only wearing contacts or only wearing glasses.

00:35 So we can just look at the total values for only contacts and only glasses, and add those two together and divide that by the total number of people in the survey, which is 3 ,203.

00:55 So you're going to end up with 253 plus 1 ,268 for your numerator, which is 1 ,521, divided by 3 ,203.

01:10 And that as a decimal is 0 .4749.

01:17 Okay, so i'm not sure whether you want fraction answers or decimals.

01:20 Your question doesn't say, so i'm going to be giving you both of them.

01:24 That's your answer for part a.

01:26 Part b, we have the probability that we have a male or where's both.

01:32 So i'll take the total from the mail row, which is the 1 ,538.

01:40 And i'll add the total from the both column, which is 545.

01:47 But what happened there is we added the number of 177 twice.

01:52 So we have to subtract it once.

01:56 And again, it's going to be out of 3 ,203.

02:02 Okay, so let me type that in.

02:10 You end up with 1 ,906 over 3 ,203.

02:15 And i'm checking to see if these simplify.

02:21 I doubt they do...

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