### Problem 3The probability of Christine getting a new job or going on vacation (or both) is 0.85. If the probability of Christine going on vacation is 0.10 and the probability of Christine getting a new job is 0.75, are the events "Christine gets a new job" and "Christine goes on vacation" mutually exclusive? Justify your answer.### Problem 4The probability that Isabelle will go trick-or-treating is 0.4. The probability that she will go trick-or-treating or watch a scary movie is 0.65. The probability of Isabelle going trick-or-treating and watching a scary movie is 0.20.a. What is the probability that Isabelle will not watch a scary movie?b. What is the probability that Isabelle will watch a scary movie but does not go trick-or-treating?### Problem 5Let the universal set $ U = \{ a, b, \text{red, blue, tan, green, } 1, 2, 4, 6 \} $ and let subsets $ A = \{ a, b, 1, 2, 4, \text{red, tan} \} $, $ B = \{ x \mid x \text{ is a color} \} $, and $ C = \{ \text{red, blue, green, } 1, 2 \} $. Find the following sets:a. $ A^c $b. $ B \cap C $c. $ A \cap C $d. $ \emptyset \cup U^c $ ---**6. Let $ U $ denote the set of Fall Centerpieces in Cathy’s Country Shop and let:**- $ F $ = The set of centerpieces that contain flowers.- $ G $ = The set of centerpieces that contain fall gourds.- $ C $ = The set of centerpieces that contain candles.**a. Using set notation (union, intersection, complement, etc.), write each subset of Cathy’s centerpieces in terms of $ F, G, $ and $ C $.**[3] i. The set of centerpieces that contain flowers or candles (or both). **Answer:** $ F \cup C $[3] ii. The set of centerpieces that contain fall gourds and candles. **Answer:** $ G \cap C $[4] iii. The set of centerpieces that do not contain all three of these items. **Answer:** $ (F \cap G \cap C)^c $[4] iv. The set of centerpieces that contain candles and fall gourds but not flowers. **Answer:** $ C \cap G \cap F^c $[3] b. Describe the set $ C^c \cap G^c $ in words (in terms of what the sets and symbols mean). **Answer:** The set of centerpieces that do not contain candles and do not contain fall gourds.---**7. Trudy has 180 Trick-or-Treat goody bags in her shop. 120 of her bags contain candy, 95 of her bags contain a small toy, and 45 of her bags contain both candy and a small toy.**[4] a. How many of her treat bags do not contain both candy and a small toy? **Answer:** 135 bags (since 180 - 45 = 135)[4] b. How many of her bags contain candy but do not contain a small toy? **Answer:** 75 bags (since 120 - 45 = 75)[4] c. How many of her bags contain a small toy or candy or both? **Answer:** 170 bags (since 120 + 95 - 45 = 170)---

Name: ### Problem 3The probability of Christine getting a new job or going
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Description: ### Problem 3The probability of Christine getting a new job or going on vacation (or both) is 0.85. If the probability of Christine going on vacation is 0.10 and the probability of Christine getting a new job is 0.75, are the events "Christine gets

The given data are: P(getting a new job or going on a vacation)=0.85 P(going on a vacation)=0.10…

Math

Probability

[8] 3. The probability of Christine getting a new job or going on vacation (or both) is .85. If the probability of Christine going on vacation is .10 and the probability of Christine getting a new job is .75, are the events “Christine gets a new job" and “Christine goes on vacation" mutually exclusive? Justify your answer. 4. The probability that Isabelle will go trick-or-treating is .4. The probability that she will go trick-or-treating or watch a scary movie is .65. The probability of Isabelle going trick-or-treating and watching a scary movie is .20. [9] a. What is the probability that Isabelle will not watch a scary movie? [4] b. What is the probability that Isabelle will watch a scary movie but does not go trick-or-treating? 5. Let the universal set U = {a, b, red, blue, tan, green, 1, 2, 4, 6} and let subsets A= (a, b, 1, 2, 4, red, tan}, B = {x|x is a color} and C= {red, blue, green, 1, 2 }. Find the following sets: [3] a. A° [3] b. Вос [3] c. AnC [3] d. Ø U U°

[8] 3. The probability of Christine getting a new job or going on vacation (or both) is .85. If the probability of Christine going on vacation is .10 and the probability of Christine getting a new job is .75, are the events “Christine gets a new job" and “Christine goes on vacation" mutually exclusive? Justify your answer. 4. The probability that Isabelle will go trick-or-treating is .4. The probability that she will go trick-or-treating or watch a scary movie is .65. The probability of Isabelle going trick-or-treating and watching a scary movie is .20. [9] a. What is the probability that Isabelle will not watch a scary movie? [4] b. What is the probability that Isabelle will watch a scary movie but does not go trick-or-treating? 5. Let the universal set U = {a, b, red, blue, tan, green, 1, 2, 4, 6} and let subsets A= (a, b, 1, 2, 4, red, tan}, B = {x|x is a color} and C= {red, blue, green, 1, 2 }. Find the following sets: [3] a. A° [3] b. Вос [3] c. AnC [3] d. Ø U U°

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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