Shoppers at? Pageturner\'s Bookstore are? tracked, with the following results: 4
ID: 2887581 • Letter: S
Question
Shoppers at? Pageturner's Bookstore are? tracked, with the following results: 42?% visit the periodicals? section, 52?% visit the fiction? section, and 22?% visit the? children's section.? Furthermore, 17?% visit the periodicals and fiction? section, 13?% visit the periodicals and the? children's section, 12?% visit the fiction and the? children's section, and 6?% visit all three sections. A shopper is randomly chosen. Complete parts? a through d.
a. Find the probability that the shopper visited the fiction or the children's section First identify the probabilities in the Venn diagram to the right and write them in decimal form. Let event P - the event that a shopper visits the periodicals section, let event Fevent that a shopper visits the fiction section, and let event C event that a shopper visits the children's section. Also, let S be the sample space Type integers or decimals. Simplity your answers.) Vil VIll The probability that the shopper visited the fiction or the children's section is Type an integer or decimal. Simplify your answer.) b. Find the probability that the shopper visited at exactly 1 of the three sections The probability that the shopper visited at exactly 1 of the three sections is (Type an integer or decimal. Simplify your answer.) c. Find the probability that the shopper did not visit any of these three sections The probability that the shopper did not visit any of these three sections is (Type an integer or decimal. Simplify your answer.) d. Find the odds in favor of the event in part (a) occurring First write an expression for the odds in favor of F U C. Select all that apply P(F U C) ? D. P(F U C)): (1-P(F U C)) E. (1- P(F U C)):P(F U C)Explanation / Answer
Dear Student Thank you for using Chegg !! From the given Venn Diagram Given P (periodicals) or P(p1) = 0.42 P (Fiction) or P(f) = 0.52 P (Childeren) or P('c) = 0.22 P (p1^f) = 0.17 P (p1^c) = 0.13 P (f^c) = 0.12 P (p^f^c) = 0.06 From Venn diagram and above data P(I) = P(p1)- P(p1^f) - P (p1^c) + P (p1^f^c) = 0.42 - 0.17 - 0.13 + 0.06 = 0.18 P (II) = P(p1^f) - P (p1^f^c) = 0.17 - 0.06 = 0.11 P(III) = P(f)- P(p1^f) - P (f^c) + P (p1^f^c) = 0.52 - 0.17 - 0.12 + 0.06 = 0.29 P (IV) = P (p1^c) - P(p1^f^c) = 0.13 - 0.06 = 0.07 P(V) = P(p1^f^c) = 0.06 P(VI) = P (f^c) - P(p1^f^c) = 0.12 - 0.06 = 0.06 P (VII) = P('c) - P(p1^c) - P(f^c) + P(p1^c^f) = 0.22 - 0.13 - 0.12 + 0.06 = 0.03 P(VIII) = 1 - P(p1VfVc) P(p1VfVc) = P(I) + P(II) + P(III) + P(IV) + P(V) + P(VI) + P(VII) = 0.8 P(VIII) = 0.2 b) Probability that shopper visited exactly one of the three sections = P(I) + P(III) + P(VII) = 0.5 c) Probablity that shopper did not visit any of the three sections = P (VIII) = 0.2 d) Odds in favoor that shopkeeper visited exactly one of three sections is Probability that shopper visited exactly one of three section / probability that shopper visited none of three section = 0.5 / 0.2 = 2.5 is 2.5 : 1 Solution