Eye Survey The table shows the results of a survey that...

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. $$\begin{array}{|l|c|c|c|c|l|} \hline & \text { Only contacts } & \text { Only glasses } & \text { Both } & \text { Neither } & \text { Total } \\ \hline \text { Male } & 64 & 841 & 177 & 456 & 1538 \\ \text { Female } & 189 & 427 & 368 & 681 & 1665 \\ \hline \text { Total } & 253 & 1268 & 545 & 1137 & 3203 \\ \hline \end{array}$$ (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.

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.
$$\begin{array}{|l|c|c|c|c|l|}
\hline & \text { Only contacts } & \text { Only glasses } & \text { Both } & \text { Neither } & \text { Total } \\
\hline \text { Male } & 64 & 841 & 177 & 456 & 1538 \\
\text { Female } & 189 & 427 & 368 & 681 & 1665 \\
\hline \text { Total } & 253 & 1268 & 545 & 1137 & 3203 \\
\hline
\end{array}$$
(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.

Key Concepts

Union and Intersection of Events

The union of events refers to the occurrence of at least one of multiple events, while the intersection represents the simultaneous occurrence of events. Calculating probabilities for unions typically involves adding individual probabilities and then subtracting the probability of their intersection to avoid double counting, as articulated in the inclusion?exclusion principle.

Complementary Events

Complementary events are pairs of outcomes where one event occurs if and only if the other does not occur. Understanding complements is useful when dealing with scenarios such as determining the probability of 'not wearing glasses', as this can be computed by subtracting the probability of wearing glasses from one.

Probability

Probability is the measure of the likelihood that an event will occur, calculated as the number of favorable outcomes divided by the total number of outcomes. This concept is fundamental in statistics and helps in quantifying uncertainty when selecting elements randomly from a dataset.

Contingency Tables

Contingency tables are a type of table in a matrix format that displays the frequency distribution of variables. They are used to summarize and analyze the relationship between two or more categorical variables, making it easier to extract probabilities from survey data or experimental outcomes.

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