STATS 3.2 3.3 4.1 4.2
(a) List an example of two events that are independent. (b) List an example of two events that are dependent.
(a)Rolling a die twice (b)Drawing one card from a standard deck, not replacing it, and then selecting another card
If two events are mutually exclusive, why is P(A and B)=0?
P(A and B)=0 because A and B cannot occur at the same time.
What are the two conditions that determine a probability distribution? Choose the correct answer below.
The probability of each value of the discrete random variable is between 0 and 1, inclusive, and the sum of all the probabilities is 1.
Of the cartons produced by a company, 5% have a puncture, 7% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner ?%
13.8 (5)+(7)-(0.4)= 13.8
What is a discrete probability distribution? What are the two conditions that determine a probability distribution?
A discrete probability distribution lists each possible value a random variable can assume, together with its probability.
In a binomial experiement, what does it mean to say that each trial is independent of the other trials?
Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials.
Determine whether the following statement is true or false. If it is false, explain why. The probability that event A or event B will occur is P(A or B)=P(A)+P(B)−P(A or B).
False, the probability that A or B will occur is P(A or B)=P(A)+P(B)−P(A and B).
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.
False. In most applications, discrete random variables represent counted data, while continuous random variables represent measured data.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, P(A|B)=P(B).
False; if events A and B are independent, then P(A and B)=P(A)•P(B).
Match n=4, n=8, n=12 with the correct graph. Each histogram shown below represents part of a binomial distribution. Each distribution has the same probability of success p but different numbers of trials n.
Histogram (a) has the number of trials n=12. Part 2 Histogram (b) has the number of trials n=4. Part 3 Histogram (c) has the number of trials n=8. Part 4 What happens as the value of n increases and the probability of success remains the same? A. As n increases, the distribution becomes more symmetric.
Identify the two events described in the study and determine if the results indicate that the events are independent or dependent. Explain your reasoning. A study found that there is no relationship between being around car batteries exposure and developing heart disease. Identify the two events.
Independent. Being around car batteries exposure does not cause heart disease.
What is the significance of the mean of a probability distribution?
It is the expected value of a discrete random variable.
Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain.
No, because the expected value may not be a possible value of x for one trial, but it represents the average value of x over a large number of trials.
A state lottery randomly chooses 7 balls numbered from 1 through 36 without replacement. You choose 7 numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x. Is the experiment binomial? Identify a success. Choose the correct answer below. Specify the values n, p, and q. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. List the possible values of the random variable x. Choose the correct answer below.
No, because the probability of success is different for each trial. The experiment is not binomial. The experiment is not binomial. The experiment is not binomial.
Can two events with nonzero probabilities be both independent and mutually exclusive?
No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
A study found that people who suffer from obstructive sleep apnea are at increased risk of having heart disease. Identify the two events described in the study. Do the results indicate that the events are independent or dependent? Identify the two events.
Sleep apnea and heart disease Dependent
Explain how the complement can be used to find the probability of getting at least one item of a particular type.
The complement of "at least one" is "none." So, the probability of getting at least one item is equal to 1−P(none of the items).
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. Click the icon to view the Venn diagram.dup
The events are mutually exclusive, since there are no movies that are rated R and are rated PG.
Decide whether the events shown in the accompanying Venn diagram are mutually exclusive. Explain your reasoning. Click the icon to view the Venn diagram.
The events are not mutually exclusive, since there is at least 1 presidential candidate who lost the popular voteis at least 1 presidential candidate who lost the popular vote and lost the election.
Determine whether the events are independent or dependent. Explain your reasoning. Returning a rented movie after the due date and receiving a late fee
The events are dependent because the outcome of returning a rented movie after the due date affects the probability of the outcome of receiving a late fee.
What is a random variable?
The outcome of a probability experiment is often a count or a measure. When this occurs, the outcome is called a random variable.
What does the notation P(B|A) mean?
The probability of event B occurring, given that event A has occurred
A physics class has 40 students. Of these, 14 students are physics majors and 15 students are female. Of the physics majors, two are female. Find the probability that a randomly selected student is female or a physics major.
The probability that a randomly selected student is female or a physics major is 0.675 p(female)+p(physics)-p(female and physics)
Determine if the statement is true or false. If the statement is false, rewrite it as a true statement. The expected value of a random variable can never be negative.
The statement is false. The expected value of a random variable can be negative.
For the given pair of events, classify the two events as independent or dependent. Having an excellent driving record getting a good rate on auto insurance
The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
For the given pair of events, classify the two events as independent or dependent. Winning $100 on your first trip to the casino Winning $100 on your second trip to the casino
The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a voter who is a registered Democrat. Event B: Randomly select a voter who is a registered member of the Green Party.
These events are mutually exclusive, since it is not possible for a voter to both be a registered Democrat and be a registered member of the Green Party.
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a female economics major. Event B: Randomly select a economics major who is 21 years old.
These events are not mutually exclusive, since it is possible to select a female economics major who is 21 years old.
What is the difference between independent and dependent events?
Two events are independent when the occurrence of one event does not affect the probability of the occurrence of the other event. Two events are dependent when the occurrence of one event affects the probability of the occurrence of the other event.
The histograms each represent part of a binomial distribution. Each distribution has the same probability of success, p, but different numbers of trials, n. Identify the unusual values of x in each histogram. Identify the unusual values of x in histogram (b). Choose the correct answer below.
X=0 X=0, X=1, X=2, X=8 X=0, X=1, X=2, X=3, X=4, X=11, AND X=12
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common.
true
About 20% of babies born with a certain ailment recover fully. A hospital is caring for six babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? What is a success in this experiment? Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. List the possible values of the random variable x.
yes Baby recovers n=6 p=0.2 q=0.8 (because 1-0.2=0.8) x=0, 1, 2,...,6
A survey asks 1000 workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?" Thirty-eight percent of those surveyed say they are reducing the amount of vacation. Ten workers participating in the survey are randomly selected. The random variable represents the number of workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment? What is a success in this experiment? Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. Specify the value of p. Select the correct choice below and fill in any answer boxes in your choice. Specify the value of q. Select the correct choice below and fill in any answer boxes in your choice. List the possible values of the random variable x.
yes Selecting a worker who is reducing the amount of vacation n=10 p=0.38 q=0.62 (because 1-0.38=0.62) x=0,1, 2,...,10
The following histograms each represent binomial distributions. Each distribution has the same number of trials n but different probabilities of success p. Match p=0.3, p=0.5, p=0.6 with the correct graph.
(a) p=0.3, (b) p=0.5, (c) p=0.6
