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5.1.3 Quiz: Probability

Question 1 of 10

\begin{tabular}{|c|c|c|}
\hline
Place & Is a city & Is in North America \\
\hline
India & & \\
\hline
Tokyo & [tex]$\checkmark$[/tex] & \\
\hline
Chicago & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Peru & & \\
\hline
Miami & [tex]$\checkmark$[/tex] & [tex]$\checkmark$[/tex] \\
\hline
Canada & & [tex]$\checkmark$[/tex] \\
\hline
Mexico & & [tex]$\checkmark$[/tex] \\
\hline
\end{tabular}

A place from this table is chosen at random. Let event [tex]A=[/tex] The place is a city.

What is [tex]P\left(A^C\right)[/tex]?

A. 4

Sagot :

GinnyAnswer
To determine the probability [tex]\( P(A^C) \)[/tex], where [tex]\( A \)[/tex] is the event that a chosen place is a city, and [tex]\( A^C \)[/tex] represents the complement of [tex]\( A \)[/tex] (i.e., the event that a chosen place is not a city), we will follow these steps:

1. Identify the Total Number of Places:

We have a total of 7 places listed in the table:
- India
- Tokyo
- Chicago
- Peru
- Miami
- Canada
- Mexico

2. Count the Number of Places That Are Cities:

From the table, the places that are cities are:
- Tokyo
- Chicago
- Miami

Thus, there are 3 places that are cities.

3. Calculate the Number of Places That Are Not Cities:

The total number of places is 7, and the number of places that are cities is 3. Therefore, the number of places that are not cities is:
[tex]\[ 7 - 3 = 4 \][/tex]

4. Determine the Probability [tex]\( P(A^C) \)[/tex]:

To find the probability [tex]\( P(A^C) \)[/tex], we need to determine the ratio of the number of places that are not cities to the total number of places. This ratio is:
[tex]\[ P(A^C) = \frac{\text{Number of places that are not cities}}{\text{Total number of places}} = \frac{4}{7} \][/tex]

The probability [tex]\( P(A^C) \)[/tex] represents the likelihood that a randomly chosen place from the table is not a city.

Given the choices provided, the answer is:
A. 4
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