TEST 2 IN QUANTATIVE REASONING VOCABULARY
What are the steps to find the median?
1. Arrange the data items in order, from smallest to largest. 2. If the number of data items is odd, the median is the data item in the middle of the list. 3. If the number of data items is even, the median is the mean of the two middle data items.
What are the steps to finding Standard deviation?
1. Find the mean of the data items 2. Find the deviation of each data item from the mean: data item − mean. 3. Square each deviation: (data item − mean) 2. 4. Sum the squared deviations: ∑(data item − mean) 2 5. Divide the sum in step 4 by n − 1, where n represents the number of data items: 6. Take the square root of the quotient in step 5. This is the standard deviation for the data set.
A standard bridge deck has ____ cards
52
Because P(E)+P(not E)=1, then P(not E)=_______ and P(E)=_______.
Because P(E)+P(not E)=1, then P(not E)= 1-P(E) and P(E)= 1-P(not E).
Probability of event B, assuming that event A has already occurred is called what?
Conditional probability
Two events are ___ if the occurrence of one of them has an effect on the probability of another
Dependent events
How is standard deviation found?
Determining how much each data item differs from the mean
Theoretical probability is based on a set of equally likely outcomes and the number of elements in the set. By contrast, ______ ____ applies to the situation in which we observe how frequently an event occurs.
Empirical probability
Denoted by E in any subset of a sample space. (The two heads and one tail)
Event
Give an example of two events that are not mutually exclusive.
Event A: Rolling a number greater than 3 on a die. Event B: Rolling the number 5 on a die.
Any occurrence for which the outcome is uncertain
Experiment
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The probability of A or B can always be found by adding the probability of A and the probability of B.
False; if probabilities of events A and B are not mutually exclusive events then the probability that A or B will occur is determined by adding their individual probabilities and subtracting the probability that A and B occur simultaneously.
If it is impossible for events A and B to occur simultaneously, the events are said to be _____. For such events, P(A or B)=_____.
If it is impossible for events A and B to occur simultaneously, the events are said to be mutually exclusive. For such events, P(A or B)= P(A) + P(B).
If it is possible for the events A and B to occur simultaneously, then P(A or B)=_______.
If it is possible for the events A and B to occur simultaneously, then P(A or B)= P(A) + P(B) - P(A and B)
If the occurrence of one event has an effect on the probability of another event, the events are said to be _______. For such events, P(A and B)=_______.
If the occurrence of one event has an effect on the probability of another event, the events are said to be dependent. For such events, P(A and B)= P(A) X P(B/A).
If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is _______
If you can choose one item from a group of M items and a second item from a group of N items, then the total number of two-item choices is MXN
If A and B are not mutually exclusive events, then it is possible for events A and B to happen simultaneously. What is this called?
Inclusive events
What are measures used to describe the spread of data items in a data set?
Measures of dispersion
What is the data item in the middle of each set of ranked, or ordered, data?
Median
What is found by adding the lowest and highest data values and dividing the sum by 2?
Midrange
What is the data value that occurs most often in a data set?
Mode
Events A and B are ____ if it is impossible for them to occur simultaneously
Mutually exclusive
How is conditional probability denoted?
P(BnA)/P(A) or P(B and A)/P(A) or P(B/A)
What is the difference between the highest and lowest data values in a data set?
Range
What are two of the most common measures of dispersion?
Range and Standard deviation
The set of all possible outcomes of an experiment, denoted by S
Sample space
Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of _______ with comic E performing first divided by _______.
Six stand-up comics, A, B, C, D, E, and F, are to perform on a single evening at a comedy club. The order of performance is determined by random selection. The probability that comic E will perform first is the number of permutations with comic E performing first divided by the total number of possible permutations.
What is a measure of dispersion that is dependent on all of the data items?
Standard deviation
The theoretical probabilities of all possible outcomes are 1.
Sum
A 5/46 lottery involves choosing 5 of the numbers from 1 through 46 and a 4/27 lottery involves choosing 4 of the numbers 1 through 27. The order in which the numbers are chosen does not matter. Which lottery is easier to win? Explain your answer.
The 4/27 lottery is easier to win because there are only 17550 possibilities, compared to the 1370754 possibilities of the 5/46 lottery.
The Powerball lottery for a certain region is set up so that each player chooses five different numbers from 1 to 59 and one Powerball number from 1 to 35. A player wins the jackpot by matching all five numbers in any order from the 1 to 59 group and matching the Powerball number. Suppose that there is a drawing in which the Powerball lottery jackpot is promised to exceed $500 million. If a person purchases 175,223,510 tickets at $2 per ticket (all possible combinations), isn't this a guarantee of winning the jackpot? Because the probability in this situation is 1, what's wrong with doing this?
The prize is shared among all winners. This person is guaranteed to win, but not guaranteed to win $500 million.
The probability of event B, assuming that event A has already occurred, is called the _____ probability of B, given A. This probability is denoted by ____.
The probability of event B, assuming that event A has already occurred, is called the conditional probability of B, given A. This probability is denoted by P(B/A).
Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.) A medical researcher needs 16 people to test the effectiveness of an experimental drug. If 43 people have volunteered for the test, in how many ways can 16 people be selected? The problem involves a ____ because the ___ of patients selected ____ matter
The problem involves a combination because the order of the patients selected does not matter
Determine whether the following statement makes or does not make sense. The formula for nCr should be used to determine how many five-letter passwords, with no repeated letters, can be formed using the letters a, b, c, d, e, f, and g.
The statement does not make sense
Determine whether the following statement makes sense or does not make sense, and explain your reasoning. Assuming that it might rain tomorrow or that it might not rain at all, the probability of it not raining tomorrow is 0.5.
The statement does not make sense because an event having two possible outcomes does not necessarily require that the outcomes are equally likely to be selected.
Determine whether the following statement makes sense or does not make sense, and explain your reasoning. I would never choose the lottery numbers 1, 2, 3, 4, 5, 6 because the probability of winning with six numbers in a row is less than winning with six random numbers.
The statement does not make sense because every combination of six numbers is equally likely to be drawn
Determine whether the statement makes sense or does not make sense. The probability that Jill will win the election is 0.7 and the probability that she will not win is 0.4
The statement does not make sense because for any event E, P(E)+P(not E)=1, and in this statement P(win)+P(not win)≠1.
Determine whether the following statement is true or false. Probability problems with the word "or" involve more than one selection.
The statement is false because "or" problems always involve only one selection.
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Permutation problems involve situations in which the order of the items does not matter.
The statement is false. Permutation problems involve situations in which the order of the items does matter.
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. When working problems involving probability with permutations, the denominators of the probability fractions consist of the total number of possible permutations.
The statement is true.
Determine whether the following statement makes sense or does not make sense, and explain your reasoning. In a group of five men and five women, the probability of randomly selecting a man is 1/2, so if I select two people from the group, the probability that both are men is (1/2)(1/2)
This statement does not make sense. The probability of select a man on the first pick is one half, but then there are only 4 men remaining out of 9 total people, so the probability of selecting another man is 4/9, not 1/2.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If one item is chosen from M items, a second item is chosen from N items, and a third item is chosen from P items, the total number of three-item choices is M+N+P.
This statement is false. To make this statement true, change "M+N+P" to "M•N•P".
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Combination problems involve situations in which the order of the items makes a difference.
This statement is false. To make this statement true, change "makes a difference" to "does not make a difference".
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. "And" probabilities can always be determined using the formula P(A and B)=P(A)•P(B).
This statement is false. "And" probabilities can be determined using the formula P(A and B)=P(A)•P(B) only if A and B are independent. Otherwise, they can be found using the formula P(A and B)=P(A)•P(B|A).
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If an event is certain to occur, its probability is 1.
This statement is true.
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sum of the probabilities of all possible outcomes in an experiment is 1.
This statement is true.
Determine whether the statement makes sense or does not make sense and explain your reasoning. The Fundamental Counting Principle can be used to determine the number of ways of arranging the numbers 1, 2, 3, 4, 5,..., 98, 99, 100.
This statement makes sense because the Fundamental Counting Principle is used to find the number of ways in which a series of successive things can occur.
The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is 17. Complete parts (a)through (d) below. a. What is the probability that the state will be hit by a major tornado two years in a row? b. What is the probability that the state will be hit by a major tornado in three consecutive years? c. What is the probability that the state will not be hit by a major tornado in the next ten years? d. What is the probability that the state will be hit by a major tornado at least once in the next ten years?
a. 0.02041 b. 0.00292 c. 0.214 d. 0.786
Eduardo, Katrina, Simone, Dawn, and Jim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. a. In how many ways can they arrive? b. In how many ways can Eduardo arrive first and Jim last? c. Find the probability that Eduardo will arrive first and Jim last
a. 120 b. 6 c. 1/20
A group consists of five Democrats and eight Republicans. Seven people are selected to attend the conference. a. In how many ways can seven people be selected from this group of thirteen? b. In how many ways can seven Republicans be selected from the eight Republicans? c. Find the probability that the selected group will consist of all Republicans.
a. The number of ways to select seven people from the group of thirteen is 1716 b. The number of ways to select seven Republicans from the group of eight Republicans is 8 c. The probability is 2/429
A standard bridge deck has 52 cards with four suits: hearts and diamonds are red, and _____ and ____ are black
clubs, spades
The ____ of an event: If the event is P(E), then the ___ is P(not E).
complement
A standard bridge deck has 52 cards with four suits: _____ and ___ are red, and clubs and spades are black
hearts, diamonds
if an event E has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, the ______ probability of event E, denoted by P(E), is: P(E), is P(E)=______/_____
if an event E has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, the theoretical probability of event E, denoted by P(E), is: P(E), is P(E)= number of outcomes in event/ total number of the possible outcome
if the occurrence of one event has no effect on the probability of another event, the events are said to be _______. For such events, P(A and B)=_______.
if the occurrence of one event has no effect on the probability of another event, the events are said to be independent . For such events, P(A and B)= P(A) + P(B).
Two events are ____ if the occurrence of either of them has no effect on the probability of the other.
independent events
If more than one data value has the highest frequency, then each of these data values is a ___. If there is no data value that occurs most often, then the data set has no ____.
mode
The number of possible combinations if r objects are taken from n items is nCr=
n!/ (n-r)!r!
The empirical probability of event E is P(E)=
observed number of times E occurs/ total number of observed occurences
The formula for nCr has the same numerator as the formula for nPr but contains an extra factor of _____ in the denominator
r!
The set of all possible outcomes of an experiment is called the ______ of the experiment.
sample space
