### 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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

### Problem 3

The 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 4

The 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 5

Let 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)

---

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