Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Probability Calculations with Mutually Exclusive and Not Mutually Exclusive Events, Exercises of Reasoning

Virginia State University (VSU)Reasoning

Solutions to various probability problems, including mutually exclusive and not mutually exclusive events. It covers various scenarios such as drawing cards from a deck, rolling dice, and selecting colors or shapes. The solutions are presented in a clear and concise manner.

Typology: Exercises

2021/2022

Uploaded on 09/12/2022

gangesha
gangesha 🇺🇸

4.6

(20)

238 documents

1 / 12

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Determinewhethertheeventsaremutually
exclusive.Explainyourreasoning.
1.drawingacardfromastandarddeckandgettinga
jackoraclub
SOLUTION:
Ajackofclubsisbothajackandaclub,sothe
eventsarenotmutuallyexclusive.
ANSWER:
notmutuallyexclusive;Ajackofclubsisbothajack
andaclub.
2.adoptingacatoradog
SOLUTION:
Acatcannotbeadog,andadogcannotbeacat,so
theeventsaremutuallyexclusive.
ANSWER:
mutuallyexclusive;Acatcannotbeadog,andadog
cannotbeacat.
3.JOBSAdelaideistheemployeeofthemonthather
job.Herrewardistoselectatrandomfrom4gift
cards,6coffeemugs,7DVDs,10pictureframes,
and3giftbaskets.Whatistheprobabilitythat
Adelaidereceivesagiftcard,coffeemug,orpicture
frame?
SOLUTION:
LeteventGrepresentreceivingagiftcard.Letevent
Crepresentreceivingacoffeemug.LeteventD
representreceivingapictureframe.
Thereareatotalof4+6+7+10+3or30items.
ANSWER:
orabout67%
4.SPORTSCARDSDarioowns145baseballcards,
102footballcards,and48basketballcards.He
selectsacardatrandomtogivetohisbrother.What
istheprobabilitythatheselectsabaseballora
footballcard?
SOLUTION:
Thereare145+102+48=195totalcards.
LetBrepresentbaseballcardsandFrepresent
footballcards.
So,theprobabilitythatDarioselectsabaseballora
footballcardis orabout84%.
ANSWER:
orabout84%
eSolutionsManual-PoweredbyCogneroPage1
12-6ProbabilityandtheAdditionRule
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Probability Calculations with Mutually Exclusive and Not Mutually Exclusive Events and more Exercises Reasoning in PDF only on Docsity!

Determine whether the events are mutually exclusive. Explain your reasoning.

  1. drawing a card from a standard deck and getting a jack or a club SOLUTION: A jack of clubs is both a jack and a club, so the events are not mutually exclusive. ANSWER: not mutually exclusive; A jack of clubs is both a jack and a club.
  2. adopting a cat or a dog SOLUTION: A cat cannot be a dog, and a dog cannot be a cat, so the events are mutually exclusive. ANSWER: mutually exclusive; A cat cannot be a dog, and a dog cannot be a cat. 3. JOBS Adelaide is the employee of the month at her job. Her reward is to select at random from 4 gift cards, 6 coffee mugs, 7 DVDs, 10 picture frames, and 3 gift baskets. What is the probability that Adelaide receives a gift card, coffee mug, or picture frame? SOLUTION: Let event G represent receiving a gift card. Let event C represent receiving a coffee mug. Let event D represent receiving a picture frame. There are a total of 4 + 6 + 7 + 10 + 3 or 30 items. ANSWER: or about 67% 4. SPORTS CARDS Dario owns 145 baseball cards, 102 football cards, and 48 basketball cards. He selects a card at random to give to his brother. What is the probability that he selects a baseball or a football card? SOLUTION: There are 145 + 102 + 48 = 195 total cards. Let B represent baseball cards and F represent football cards. So, the probability that Dario selects a baseball or a football card is or about 84%. ANSWER: or about 84%
  1. CLUBS According to the table, what is the probability that a student in a club is a junior or on the debate team? SOLUTION: Because some juniors are on the debate team, these events are not mutually exclusive. Use the rule for two events that are not mutually exclusive. The total number of students is 100. ANSWER: or about 44% 6. KITTENS Ruby’s cat had 8 kittens. The litter included 2 gray females, 3 mixed-color females, 1 gray male, and 2 mixed-color males. Ruby wants to keep one kitten. What is the probability that she randomly chooses a kitten that is female or gray? SOLUTION: Because some of Ruby's kittens are both gray and female, these events are not mutually exclusive. Use the rule for two events that are not mutually exclusive. The total number of kittens is given as 8. P (gray or female) = P (gray) + P (female) – P (gray and female) So, the probability that Ruby randomly chooses a kitten that is female or gray is or 75%. ANSWER: or 75%
  1. selecting a number at random from integers 1 to 20 and getting an even number or a number divisible by 3 SOLUTION: 18 is between 1 and 20, and is both even and divisible by 3. Because these two events can happen at the same time, these are not mutually exclusive. Use the rule for two events that are not mutually exclusive. Let e represent an even number and d represent divisible by 3. ANSWER: not mutually exclusive; or 65%
  2. tossing a coin and getting heads or tails SOLUTION: Because these two events cannot happen at the same time, these are mutually exclusive. Let event T represent getting tails. Let event H represent getting heads. ANSWER: mutually exclusive; 100%
  3. drawing an ace or a heart from a standard deck of 52 cards SOLUTION: Because these two events can happen at the same time, these are not mutually exclusive. Use the rule for two events that are not mutually exclusive. ANSWER: not mutually exclusive; or 30.8%
  4. rolling a pair of number cubes and getting a sum of either 6 or 10 SOLUTION: Because these two events cannot happen at the same time, they are mutually exclusive. The total number of possible outcomes when rolling a pair of number cubes is 36. ANSWER: mutually exclusive; or about 22.2%
  1. SPORTS The table includes all of the programs offered at a sports complex and the number of participants aged 14–16. What is the probability that a player is 14 or plays basketball? SOLUTION: Because some 14-year-old participants play basketball, these events are not mutually exclusive. Use the rule for two events that are not mutually exclusive. The total number of players is 300. ANSWER: 56%
    1. MODELING An exchange student is moving back to Italy, and her homeroom class wants to get her a going-away present. The teacher takes a survey of the class of 32 students and finds that 10 people choose a card, 12 choose a T-shirt, 6 choose a video, and 4 choose a bracelet. If the teacher randomly selects the present, what is the probability that the exchange student will get a card or a bracelet? SOLUTION: Let event C represent getting a card. Let event B represent getting a bracelet. ANSWER: or about 43.8%
    2. Talia is playing a board game where rolling two dice determines the number of spaces she moves. In Talia’s current position, she needs to roll at least a sum of 9 to win. What is the probability that Talia will win on her next turn? SOLUTION: There are a total of 36 possible outcomes when two dice are rolled. ANSWER:
  1. P (blue or yellow) SOLUTION: There are 30 total tortilla chips in the bowl. ANSWER:
  2. P (yellow or not blue) SOLUTION: "Not blue" means it can be either red or yellow. There are 30 total tortilla chips in the bowl. ANSWER:
  3. P (red or not yellow) SOLUTION: "Not yellow" means it can be red or blue. There are 30 total tortilla chips in the bowl. ANSWER:
    1. EDUCATION Max surveyed 200 students at his school to determine how many nights per week they do homework. His results are shown in the table. a. What is the probability that a randomly chosen student does homework at least 3 nights per week? b. What is the probability that a randomly chosen student does homework no more than 3 nights per week? SOLUTION: a. b. ANSWER: a. b.
  1. TILES Kirsten and José are playing a game. Kirsten places tiles numbered 1 to 50 in a bag. José selects a tile at random. If he selects a prime number or a number greater than 40, then he wins the game. What is the probability that José will win on his first turn? SOLUTION: There are 50 numbered tiles in all, with 15 prime numbers, 10 numbers greater than 40, and 3 numbers that are both prime and greater than 40. ANSWER:
  2. ERROR ANALYSIS George and Aliyah are determining the probability of randomly choosing a blue or red marble from a bag of 8 blue marbles, 6 red marbles, 8 yellow marbles, and 4 white marbles. Is either of them correct? Explain. SOLUTION: Aliyah is correct. To find the probability of blue or red, the individual probabilities should be added because the events are mutually exclusive. ANSWER: Aliyah; to find the probability of blue or red, the individual probabilities should be added because the events are mutually exclusive. REASONING Determine whether the following are mutually exclusive. Explain.
  3. choosing a quadrilateral that is a square and a quadrilateral that is a rectangle SOLUTION: If the two events cannot happen at the same time, they are mutually exclusive. Because squares are rectangles, but rectangles are not necessarily squares, a quadrilateral can be a square and a rectangle, and a quadrilateral can be a rectangle but not a square. They are not mutually exclusive. ANSWER: Not mutually exclusive; sample answer: Because squares are rectangles, but rectangles are not necessarily squares, a quadrilateral can be a square and a rectangle, and a quadrilateral can be a rectangle but not a square.
  4. choosing a triangle that is equilateral and a triangle that is equiangular SOLUTION: If the two events cannot happen at the same time, they are mutually exclusive. If a triangle is equilateral, it is also equiangular. The two can never be mutually exclusive. ANSWER: Not mutually exclusive; sample answer: If a triangle is equilateral, it is also equiangular. The two can never be mutually exclusive.
  1. Visitors to a school carnival throw a dart at a rectangular target in order to win prizes. The prizes are determined by the row and column in which the dart lands, as shown in the diagram. Tamiko throws a dart that lands at random on the target. Which is closest to the probability that she wins 3 tickets or a T-shirt? A 22% B 40% C 54% D 72% SOLUTION: So, the correct answer is choice D. ANSWER: D
    1. The spinner shown here is divided into 8 equal sectors. Elliott spins the spinner one time. What is the probability that the pointer lands on an odd number or a blue sector? A B C D E SOLUTION: Because it is possible to land on a blue sector that is an odd number on the same spin, these events are not mutually exclusive. Use the rule for events that are not mutually exclusive and the fact that there are 8 sectors of the spinner. P (odd number or blue sector) = P (odd number) + P (blue sector) – P (odd number and blue sector) = = The probability that the spinner lands on an odd number or a blue sector is. So, the correct answer is choice D. ANSWER: D
    2. Chelsea has a piece of fabric with the dimensions shown below. She spreads out the fabric on a table and then accidentally lets a drop of ink fall onto the fabric.

Assuming the ink lands at a random point on the fabric, which is closest to the probability that it lands in the white row or checkerboard column? A 42% B 38% C 25% D 4% SOLUTION: Because it is possible for the ink to drop on a piece of the fabric that is both white and checkerboard, these events are not mutually exclusive. The white section is represented by the area of a 36-by-5-inch rectangle. The checkerboard column is represented by the area of a 6-by-20 inch rectangle. Use the rule for events that are not mutually exclusive and the fact that the total area of the fabric is 36 · 20 or 720 square inches. P (white or checkerboard) = P (white) + P (checkerboard) – P (white and checkerboard) = = = = The probability that Chelsea drops a spot of ink on a white row or the checkered column is or about 38%. So, the correct answer is choice B. ANSWER: B

  1. A single number cube is rolled. Find each probability. a. P (3 or 5) b. P (at least 4) SOLUTION: a. b. There are 6 total possible outcomes, with 3 of them favorable: 4, 5, and 6. So, the probability of rolling at least a 4 is. ANSWER: a. b.