**Probability and Events: Understanding Independence and Mutual Exclusivity**- **Dependent Events:** **Question:** True or False: If Event A is eating a red candy from a new bag of Skittles and Event B is pulling a second Skittle from the same bag that is also red, Event A and Event B are dependent. **Explanation:** Events are considered dependent if the occurrence of one affects the probability of the other. In this case, removing a Skittle affects the remaining number and types of Skittles, making the events dependent.- **Independent Events:** **Question:** True or False: If Event A is Tina being the first woman to finish the 2020 Boston Marathon and Event B is Tina being the first woman to finish the 2021 New York Marathon, Event A and Event B are independent. **Explanation:** Events are independent if the occurrence of one does not affect the probability of the other. These events are not related in terms of how one impacts the likelihood of the other occurring.- **Mutually Exclusive Events (Standard Deck of Cards):** **Question:** True or False: Selecting a king or a spade from a standard deck of cards are mutually exclusive events. **Explanation:** Events are mutually exclusive if they cannot occur at the same time. In this case, you can have a king that is also a spade, so these events are not mutually exclusive.- **Mutually Exclusive Events (Building Homes):** **Question:** True or False: Building a 1500 square-foot home or a 2100 square-foot home on your new single-home property are mutually exclusive events. **Explanation:** These events are mutually exclusive because you cannot build both a 1500 square-foot and a 2100 square-foot home on the same single-home property at the same time. They cannot occur simultaneously.

Introduction: Two events are said to be independent if the occurrence of one does not affect the…

True or False: If Event A is eating a red candy from a new bag of Skittles and Event B is pulling a second Skittle from the same bag that is also red, Event A and Event B are dependent. True or False: If Event A is Tina is the first woman to finish the 2020 Boston Marathon and Event B is Tina is the first woman to finish the 2021 New York Marathon, Event A and Event B are independent. True or False: Selecting a king or a spade from a standard deck of cards are mutually exclusive events. True or False: Building a 1500 square-foot home or a 2100 square-foot home on your new single-home property are mutually exclusive events.

True or False: If Event A is eating a red candy from a new bag of Skittles and Event B is pulling a second Skittle from the same bag that is also red, Event A and Event B are dependent. True or False: If Event A is Tina is the first woman to finish the 2020 Boston Marathon and Event B is Tina is the first woman to finish the 2021 New York Marathon, Event A and Event B are independent. True or False: Selecting a king or a spade from a standard deck of cards are mutually exclusive events. True or False: Building a 1500 square-foot home or a 2100 square-foot home on your new single-home property are mutually exclusive events.

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...

See similar textbooks

Similar questions

Can babies reason probabilistically? A study investigates this by showing ten- to twelve-month-old infants two jars of lollipop-shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their “preferred” color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their probability of getting the preferred color; each jar had 12 in the preferred color and either 4 or 36 in the other color. Babies choosing randomly or based on the absolute number of their preferred color would choose equally between the two jars, while babies understanding probability would more often choose the jar with the higher proportion of their preferred color. Of the 24 infants studied, 18 chose the jar with the higher proportion of their preferred color. Are infants more likely to choose the jar with the higher proportion of their preferred color? a.)State the null and alternative…
Event A occurs with probability 0.2. Event B occurs with probability 0.3. Event C occurs with probability 0.4. If A,B, and C are disjoint, then: A) P(A or B or C) = 0.9. B) P(A or C) = 0.6. C) P(A or B) = 0.5. D) All of the answer options are correct.
Suppose you have the social network like in the following picture. The circles are people and the edges are interactions between people. Suppose the person in the centre gets a virus. In each interaction, there is a 4/5 probability of passing on the virus. a. What's the probability that only 1 person has the virus? b. What's the probability that only 2 people get the virus? c. What's the probability that only 3 people get the virus?
Part 1:There are 90 students in our Foundation program. All of these take some combination of Maths, Chemistry or Biology. The number who take Chemistry is 44; the number who take Biology is 50; and 50 take Maths. The number who take Maths and Biology is 20; the number who take Chemistry and Biology is 24, and there are 20 who take Maths only and 15 who take Biology only. a) Find the probability that a student picked at random studies only Chemistry. b) Find the probability that a student picked at random studies all three courses. c) Find the probability that a student picked at random studies Chemistry given that the student is studying Maths. pleas answer through a vandiagram and explain how you go each number inside the van digrame . thanks
On Mr. Casper’s debate team at Thunderbird High School, 20% of themembers are Sophomores, 35% are Juniors and 45% are Seniors. A teammember is selected randomly to give the closing argument for the team. If asophomore gives the closing argument, the team has a probability of 0.25 ofwinning the debate. If a junior gives the closing argument, the probability ofwinning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. (b) Describe the design of a simulation to estimate the probability that aSophomore is never selected to give the closing argument in the next 5 debates.Explain clearly how you would use a table of random digits to carry out thesimulation. (c) The dotplot below shows thenumber of sophomores chosen in 50 simulated sets of 5 debates in which 20% of thetime a Sophomore is selected and 80% of the time a Junior or Senior is selected to givethe closing argument for the team. In the next 5 debates, a sophomore…
2. (For this problem, leave your answers in Combinatorics format – do NOT simplify). Aconference is being held that faculty members from the IST department have beeninvited. There are 23 female and 19 male faculty members. Six members are randomlyselected. What is the probability of that?a. an equal number of men and women are selected?b. there are at least 4 men selected.c. no women are selected.d. no more than 4 women are selected.
Consider three football teams A, B and C. In a regular game, A beats B with probability p and beatsC with probability q. C is a better team than B, so p > q. To win the tournament, A needs to wintwo games in a row out of three games against B and C, and it can’t play two games in a row againstthe same team. A can either select to play these three games as B − C − B or C − B − C. Showthat A maximizes the probability of winning the tournament by playing against the better team C,twice.
4. A company evaluates its potentialnew employees using three criteria. A: The applicant has a minimum college GPA of 3.0. B: The applicant has relevant work experience. C: The applicant has a sufficient score on an aptitude test. Write the event that an applicant meets a ll three criteria as a union or intersection of A, B, and C. Write the event that an applicant meets at lea st one of the three criteria as a union or intersection of A, B, a. b. and C.
3. a. Explain in your own words what it means for two events to be mutually exclusive. b. If events A and B are mutually exclusive, P(A)=0.3, and P(B)=0.4, what is P(AUB)? c. If P(A)=7/10, P(B)=3/10, and P(AUB)=7/10, is it possible for events A and B to be mutually exclusive? Why or why not?
Suppose we have a deck of cards, but some of the cards are missing. That is, instead of 52 cards, we have 48 cards. My friend wants to play a magic trick - he wants me to pick a card, remember it, put it back in the deck, then shuffle the deck. He claims he can find that card. Clearly, my friend keeps track of my card somehow, but if he did not keep track, and the cards were perfectly randomized, what would be the probability that he would select my card from the deck? Round your answer to 4 decimal places. Recall Canvas truncates trailing Os automatically without loss of marks - that means if you enter something like 0.5000, Canvas changes it to 0.5, and you do not lose marks as a result.
In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week. Each bet is classified according to two variables: result of picking the Crush ("Crush won" or "Crush lost") and bet placed the following week ("Picked Crush to A win" or "Picked Crush to lose"). In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent. Round your answers to…
5. Consider the 3-component system in the figure. Every month, component c₁ fails with probability p₁ = 3.3%, components C₂ and c3 fail with probability P₂ = P3 = 30%. All failures are independent, and the failed components are repaired at the end of the month. The system fails when, in the block diagram, origin and destination are not connected. origin C1 C₂ C3 destination a) What is the probability of a system failure, every month? Are system failures at different months independent? Let T₁ indicate the month of the first system failure, T₂ the month of the second system failure, Ty the month of the y system failure. Let µy, Oy, Sy define the mean, standard deviation and the coefficient of variation of Ty, respectively. a) Compute μ₁, M2, M3; O₁, O2, O3; 81, 82, 83. b) Can you explain the trend in the mean, standard deviation and coefficient of variation? I.e., why is that quantity going down, stay constant or going up? c) Can you guess what μ, ∞, S∞ are? Are they going to zero, to…