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.
