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Conditional Probability

Name: [tex]$\qquad$[/tex]

The set of data in the table below shows the results of a survey on the number of messages that people ages text on their cell phones each month.

\begin{tabular}{|c|c|c|c|}
\hline \multicolumn{4}{|c|}{ Text Messages per Month } \\
\hline Age Group & [tex]$0-10$[/tex] & [tex]$11-50$[/tex] & Over 50 \\
\hline [tex]$15-18$[/tex] & 4 & 37 & 68 \\
\hline [tex]$19-22$[/tex] & 6 & 25 & 87 \\
\hline [tex]$23-60$[/tex] & 25 & 47 & 157 \\
\hline
\end{tabular}

If a person from this survey is selected at random, what is the probability that the person texts over 50 times per month given that the person is between the ages of 23 and 60?

1) [tex]$\frac{157}{229}$[/tex]

2) [tex]$\frac{157}{312}$[/tex]

3) [tex]$\frac{157}{384}$[/tex]

4) [tex]$\frac{157}{456}$[/tex]

Sagot :

GinnyAnswer
To solve this question, we need to find the conditional probability that a person texts over 50 messages per month given that the person is between the ages of 23 and 60.

Here's a step-by-step solution:

1. Identify the given data:
- We are given the age group 23-60 and the corresponding number of people who text 0-10, 11-50, and over 50 messages per month.
- Specifically, for the age group 23-60:
- 0-10 messages: 25 people
- 11-50 messages: 47 people
- Over 50 messages: 157 people

2. Calculate the total number of people in the age group 23-60:
- Total number of people = Number of people texting 0-10 + Number of people texting 11-50 + Number of people texting over 50
- Total number of people = 25 + 47 + 157

3. Calculate the result:
- Total number of people in the age group 23-60 = 229

4. Identify the number of people texting over 50 messages per month:
- From the given data, the number of people texting over 50 messages per month in the age group 23-60 is 157.

5. Calculate the conditional probability:
- The probability that a person texts over 50 messages per month given that the person is between the ages of 23 and 60 is the ratio of the number of people who text over 50 messages to the total number of people in that age group.
- Probability = Number of people texting over 50 messages in the age group 23-60 / Total number of people in the age group 23-60
- Probability = 157 / 229

6. Final result:
- The probability that a person texts over 50 messages per month given that the person is between the ages of 23 and 60 is [tex]\(\frac{157}{229}\)[/tex].

Therefore, the correct answer is:

1) [tex]\(\frac{157}{229}\)[/tex]
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