In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D) = 0.750, where D is directly in person. If someone is randomly selected, what does P (D) represent, and what is its value? What does P(D) represent? O A. P(D) is the probability of randomly selecting someone who chooses a direct in-person encounter as the most fun way to flirt. O B. P(D) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. O C. P(D) is the probability of randomly selecting someone who did not participate in the survey. O D. P(D) is the probability randomly selecting someone who did not have a preference in regards to the most fun way to flirt. P(D) = (Simplify your answer.)

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Chapter9: Counting And Probability
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### Understanding Probabilities in Survey Responses

In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it was found that \( P(D) = 0.750 \), where \( D \) is defined as a direct in-person encounter. If someone is randomly selected, what does \( P(\overline{D}) \) represent, and what is its value?

#### Question: What does \( P(\overline{D}) \) represent?

**Options:**
- **A.** \( P(\overline{D}) \) is the probability of randomly selecting someone who chooses a direct in-person encounter as the most fun way to flirt.
- **B.** \( P(\overline{D}) \) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt.
- **C.** \( P(\overline{D}) \) is the probability of randomly selecting someone who did not participate in the survey.
- **D.** \( P(\overline{D}) \) is the probability of randomly selecting someone who did not have a preference in regards to the most fun way to flirt.

#### Solution:
\[ P(\overline{D}) = 1 - P(D) \]

Given:
\[ P(D) = 0.750 \]

\[ P(\overline{D}) = 1 - 0.750 = 0.250 \]

So, \( P(\overline{D}) \) represents the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt.

Therefore, the correct answer is:

**B.** \( P(\overline{D}) \) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt.

\[ P(\overline{D}) = 0.250 \]

*(Simplify your answer.)*
Transcribed Image Text:### Understanding Probabilities in Survey Responses In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it was found that \( P(D) = 0.750 \), where \( D \) is defined as a direct in-person encounter. If someone is randomly selected, what does \( P(\overline{D}) \) represent, and what is its value? #### Question: What does \( P(\overline{D}) \) represent? **Options:** - **A.** \( P(\overline{D}) \) is the probability of randomly selecting someone who chooses a direct in-person encounter as the most fun way to flirt. - **B.** \( P(\overline{D}) \) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. - **C.** \( P(\overline{D}) \) is the probability of randomly selecting someone who did not participate in the survey. - **D.** \( P(\overline{D}) \) is the probability of randomly selecting someone who did not have a preference in regards to the most fun way to flirt. #### Solution: \[ P(\overline{D}) = 1 - P(D) \] Given: \[ P(D) = 0.750 \] \[ P(\overline{D}) = 1 - 0.750 = 0.250 \] So, \( P(\overline{D}) \) represents the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. Therefore, the correct answer is: **B.** \( P(\overline{D}) \) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. \[ P(\overline{D}) = 0.250 \] *(Simplify your answer.)*
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