Two hundred adults age 18 to 29 were polled regarding their use of various social media websites, and the resulting data appears in the diagram below. LetF=theevent that the person uses social media website F, and T = the event that a person uses social media website T. A person from this survey is randomly chosen. Complete parts (a) through (c) below. **Find \( P(F' \mid T') \).**\[ P(F' \mid T') = \] ☐ (Simplify your answer.)**What does this number represent?**- **A.** This is the probability that a person does not use either social media websites.- **B.** This is the probability that a person does not use social media website F, given that the person does not use social media website T.- **C.** This is the probability that a person does not use social media website T, given that the person does not use social media website F.- **D.** This is the probability that a person uses some other social media website. **Title:** Understanding Conditional Probability through Social Media Usage**Summary:** A survey of 200 adults aged 18 to 29 explored their use of two social media websites, F and T. The results are depicted in a Venn diagram, where F and T represent users of each website.**Venn Diagram Explanation:**- 124 people use only website F.- 9 people use only website T.- 20 people use both websites F and T.**Tasks:****1. Conditional Probability Formula Selection**For events A and B, with \( n(B) > 0 \), the formula for the conditional probability \( P(A|B) \) determines how likely A is given that B has already occurred. Identify the correct formula from the choices:- \( \text{A. } P(A|B) = \frac{n(B)}{n(A \cap B)} \)- \( \text{B. } P(A|B) = \frac{n(A \cap B)}{n(A)} \)- \( \text{C. } P(A|B) = \frac{n(A \cap B)}{n(B)} \) *(Correct Answer)*- \( \text{D. } P(A|B) = \frac{n(A \cup B)}{n(B)} \)- \( \text{E. } P(A|B) = n(A \cup B) \cdot n(B) \)- \( \text{F. } P(A|B) = n(A \cap B) \cdot n(B) \)**2. Calculation and Interpretation:****a. Find \( P(F|T) \)**Calculate the probability that a person uses social media website F given that they use website T.- \( P(F|T) = \frac{n(F \cap T)}{n(T)} = \frac{20}{29} \)*Interpretation:* This figure represents the probability that a person uses website F given that they already use website T.**b. Find \( P(T|F) \)**Calculate the probability that a person uses social media website T given that they use website F.- \( P(T|F) = \frac{n(F \cap T)}{n(F)} = \frac{20}{144} \)*Interpretation:*This figure indicates the probability

Answered: Image /qna-images/answer/5b672e7a-3618-4140-b256-bc6a251d40bd.jpg

Two hundred adults age 18 to 29 were polled regarding their use of various social media websites, and the resulting data appears in the diagram below. Let F = the event that the person uses social media website F, and T = the event that a person uses social media website T. A person from this survey is randomly chosen. Complete parts (a) through (c) below. 124 20 47 For events A and B, with n(B) > 0, the conditional probability of A given B, denoted P(A|B), is given by which formula below? n(B) n(ANB) O A. P(A|B) = n(ANB) O B. P(A|B) = n(A) n(AUB) n(B) n(ANB) OC. P(A|B) = n(B) O D. P(A|B) = O E. P(A|B) = n(AUB) • n(B) O F. P(A|B) = n(ANB) • n(B) a. Find P(F|T). P(F|T) = (Simplify your answer.) What does this number represent? O A. This is the probability that a person uses both social media websites, F and T. O B. This is the probability that a person uses social media website F, given that the person uses social media website T. OC. This is the probability that a person uses social media website T, given that the person uses social media website F. O D. This is the probability that a person uses at least one social media website, F or T. b. Find P(T|F). P(T|F) = (Simplify your answer.) What does this number represent? O A. This is the probability that a person uses social media website T, given that the person uses social media website F. O B. This is the probability that a person uses both social media websites, F and T. O C. This is the probability that a person uses social media website F, given that the person uses social media website T. O D. This is the probability that a person uses at least one social media website, F or T.

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...