A poll of 100 senior citizens in a retirement community asked about the types of electronic communication they used. The table shows the joint and marginal frequencies from the poll results.

If you are given that one of the people polled uses text messaging, what is the probability that the person is also using e-mail? Express your answer as a decimal. If necessary, round your answer to the nearest hundredth.

\begin{tabular}{|c|c|c|c|}
\hline & Yes & No & Total \\
\hline Yes & 0.17 & 0.66 & 0.83 \\
\hline No & 0.11 & 0.06 & 0.17 \\
\hline Total & 0.28 & 0.72 & 1 \\
\hline
\end{tabular}



Answer :

To determine the conditional probability that a senior citizen uses email given that they use text messaging, we can use the provided data. Let's walk through the steps to solve this problem.

1. Understand the given information:
- We have a table of joint and marginal frequencies for the poll results.
- The relevant pieces of information are:
- The probability that a person uses both text messaging and email is 0.17.
- The probability that a person uses text messaging is 0.83.

2. Define the conditional probability:
- The conditional probability of event A given event B is denoted as P(A|B) and is calculated using the formula:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
Here, event A is "using email" and event B is "using text messaging".

3. Substitute the given values into the formula:
- [tex]\( P(\text{A} \cap \text{B}) = \text{Probability of using both email and text messaging} = 0.17 \)[/tex]
- [tex]\( P(\text{B}) = \text{Probability of using text messaging} = 0.83 \)[/tex]

4. Calculate the conditional probability:
[tex]\[ P(\text{using email} \mid \text{using text messaging}) = \frac{0.17}{0.83} = 0.20481927710843376 \][/tex]

5. Round the result to the nearest hundredth:
- To round 0.20481927710843376 to the nearest hundredth, we look at the third decimal place, which is 4.
- Since 4 is less than 5, we round down, making the result 0.20.

Conclusion:
The probability that a senior citizen uses email given that they use text messaging is approximately 0.20.