PSYC 7302 Mod. 1/2

A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment? A. S = {F, PF, PPF, PPP} B. S= {F, PF, PPF} C. S = {F, FP, FFP, FFF} D. S={P,PP,PPP} E. S ={PPP, FPP, PFP, PPF, FFP, FPF, PFF, FFF}

A. S = {F, PF, PPF, PPP}

In 2012, researchers working with a very large population of health records found that 9.3% of all Americans had diabetes (source: National Diabetes Statistics Report, 2014). Suppose a medical researcher randomly selects two individuals from a large population. Let A represent the event "the first individual has diabetes." Let B represent the event "the second individual has diabetes." True or false? A and B are independent events. A. True B. False

A. True

In the population, 8% of males have had a kidney stone. Suppose a medical researcher randomly selects two males from a large population. Let A represent the event "the first male has had a kidney stone." Let B represent the event "the second male has had a kidney stone." True or false? A and B are independent events. A. True B. False

A. True

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% chance of experiencing both side effects. What is the probability of experiencing neither of the side effects? A. 0.10 B. 0.40 C. 0.45 D. 0.70 E. 0.85

C. 0.45

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% chance of experiencing both side effects. What is the probability of experiencing nausea or a decrease in sexual drive? A. 0.10 B. 0.40 C. 0.55 D. 0.70 E. 0.85

C. 0.55

An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20. What is the probability of a random student being male or between the ages of 18 and 20? A. 0.22 B. 0.25 C. 0.70 D. 0.95

C. 0.70

A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl? A. 0.5 B. 0.125 C. 0.75 D. 0.875

C. 0.75

For a criminal trial, 8 active and 4 alternate jurors are selected. Two of the alternate jurors are male and two are female. During the trial, two of the active jurors are dismissed. The judge decides to randomly select two replacement jurors from the 4 available alternates. What is the probability that both jurors selected are female? A. 1⁄2 B. 1⁄4 C. 1⁄6 D. 1/12

C. 1⁄6

Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are freshmen and two are sophomores. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor decides to randomly select two of the four wait list students and gives them a seat in the class. What is the probability that both students selected are freshmen? A. 1⁄2 B. 1⁄4 C. 1⁄6 D. 1/12

C. 1⁄6

A person in a casino decides to play blackjack until he wins a game, but he will not play more than 3 games. Let W denote a win and L denote a loss. What is the sample space for this random experiment? A. S = {WWW, WWL, WLW, , WLL, LWW, LWL, LLW, LLL} B. S={W,LW,LLW} C. S = {W, LW, LLW, LLL} D. S={W,WW,WWW} E. S = {W, WL, WWL, WWW}

C. S = {W, LW, LLW, LLL}

A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment? A. {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF} B. {S, FS, FFS} C. {S, FS, FFS, FFF} D. {S, SS, SSS} E. {S, SF, SSF, SSS}

C. {S, FS, FFS, FFF}

What is the difference between a closed question and an open-ended question?

Closed ended questions give the participant a selection of answers to choose from while open ended questions allow for the participant to answer as they see fit

The probability that an event will not occur is referred to as the __________ of that event.

Complement

In 2009, a local university reported that 67% of students participated in extracurricular activities. The same University reported in 2010 that only 51% of students participated in extracurricular activities. What is the probability that a randomly chosen student participated in extracurricular activities in both 2009 and 2010.

0.342

Marsha is considering her chances of meeting an eligible bachelor that is both intelligent and attractive. The probability of him being intelligent is P(I)=20%, attractive P(A)=50% or both intelligent and attractive 5%. What is the probability of Marsha meeting someone who is not attractive or intelligent?

0.35

A poll conducted in 1996 found that only 27% of U.S. adults believed same-sex marriages should be recognized by law. In 2016, the same poll estimated that 61% of U.S. adults said that marriages between same-sex couples should be recognized by the law as valid, with 33% of people against same-sex marriage, and 6% of people indifferent to the matter. What is the probability that two randomly chosen U.S. adults support same-sex marriage as recognized by law?

0.41

A couple decides to adopt 3 cats from the shelter. If there is an equal likelihood of the cats at shelter being male or female, and cats are randomly chosen, what is the probability that at least one of the cats will be a male?

0.875

When determine the probability of P(A OR B) in the case when A and B are disjoint events, what does P (A AND B) equal? Are these two events independent?

0; No

A couple decides to have three children. Let A define the event that the couple has at least 1 girl. What are the possible outcomes for this event? (G=girl, B=boy) A. {G, BG, BBG} B. {G, GG, GGG} C. {BBB, BBG, BGB, GBB, GGB, GBG, BGG, GGG} D. {GGG, GGB, GBG, BGG, GBB, BGB, BBG} E. {GBB, BGB, BBG}

D. {GGG, GGB, GBG, BGG, GBB, BGB, BBG}

Rule 1: Existence

For any event A, 0 ≤ P(A) ≤ 1. You can't have less than 0 chance and you can't have more chance than certainty.

Rule 5: The Multiplication Rule for Independent Events

If A and B are two independent events, then P(A and B) = P(A) * P(B). If two things happen together only by chance we multiple the probabilities to detect the chance of the joint event.

Events are considered to be __________ if one event occurring has no effect on the probability of a second event occurring.

Independent

When events cannot possibly occur together, they are called ___________.

Independent

__________ is drawing conclusions about a population.

Inference

54% of students in A University are female. Last year, 64% of all students chose to order meal plans, while 23% of male students did not. What percentage of female students ordered meal plans last year, assuming sex and meal plan are independent:

41%

If P(A and B) equals zero then: A and B are independent A and B are disjoint and dependent

A and B are disjoint and dependent

For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of 0.99 independently of the others. What is the probability that when a theft occurs, all four systems will detect it? A. (0.99) 4 B. (0.99) * 4 C. (0.01) 4 D. 4 * (0.01) * (0.99) 3

A. (0.99) 4

A fair four-sided die, where each face is represented by a different digit between 1 and 4, is rolled 5 times. What is the probability of rolling 5 ones in a row? A. (1/4) 5 B. (1/4) * 5 C. (3/4) 5 D. 5*(3/4)*(1/4)4 E. 5*(1/4)*(3/4)4

A. (1/4) 5

Let A and B be two disjoint events such that P(A) = 0.20 and P(B) = 0.60. What is P(A and B)? A. 0 B. 0.12 C. 0.68 D. 0.80

A. 0

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% chance of experiencing both side effects. What is the probability of experiencing only nausea? A. 0.05 B. 0.10 C. 0.20 D. 0.35

A. 0.05

An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20. What is the probability of a random student being female between the ages of 18 and 20? Assume P(F) = P(not M). A. 0.15 B. 0.16 C. 0.30 D. 0.40

A. 0.15

Rule 2: Total Probability

P(S) = 1; that is, the sum of the probabilities of all possible outcomes is 1. In any single situation, the probability of any collection of events can't be greater than 1.

The following probabilities are based on data collected from U.S. adults during the National Health Interview Survey 2005-2007. Individuals are placed into a weight category based on weight, height, gender and age. Underweight: 0.019 Healthy Weight: 0.377 Over Weight: 0.35 Obese: 0.254 Based on this data, what is the probability that a randomly selected U.S. adult who weighs more than the healthy weight range is obese? A. 0.421 B. 0.254 C. 0.725 D. 0.258

A. 0.421

According to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (N) and a 50% chance of experiencing decreased sexual drive (D). The information also states that there is a 15% chance of experiencing both side effects. What formula will give you the probability of experiencing neither of these side effects? A. P("not N" and "not D") B. P(N or D) C. 1−P(NandD) D. 1 − P("not N" and "not D") E. P(N and D)

A. P("not N" and "not D")

To estimate the probability of event A, written P(A), we may repeat the random experiment many times and count the number of times event A occurs. Then P(A) is estimated by the ratio of the number of times A occurs to the number of repetitions, which is called the _____________ of even A.

relative frequency

A 2016 poll of US adults estimated that 56% of US adults feel that the laws covering the sale of fire arms should be made more strict, with 34% feeling they should be made less strict and 10% feeling they should be kept the same. What is the probability that two randomly chosen US adults support stricter gun control laws?

0.3136

According to a recent study on asthma interventions, albuterol breath actualized nebulization cause elevated heart rate (H) in 25% of patients and nausea (N) in 12% of patients. 5% of albuterol users experience both side effects. What percentage of people experience either or both side effects?

0.32

According to the drugfacts.com, when taking Methadone, there is a 40% chance of experiencing fatigue (F) and a 30% chance of experiencing decreased appetite (A). The information also states that there is a 20% chance of experiencing both side effects. What is the probability of not experiencing either side effect?

.10

When a certain female randomly reaches into their closet for a pair of shoes, 75% of the time she will grab a black pair and 55% of the time they will be summer shoes (winter and summer are the only kinds). Assuming the color and season are independent, what is the approximate probability that she will grab a pair that is winter and not black

.1125

A True/False quiz has three questions. When guessing, the probability of getting a question correct is the same as the probability of getting a question wrong. What is the probability that a student that guesses gets at least 2 questions correct? (Give your answer to 2 decimal places)

.50

The probability that an event will occur is between __________ and 1.

0

A television company surveyed their customers in 2015, 37% of their customers were happy with their current service. The same company surveyed their customers in 2016 and 52% of their customers were happy. What is the probability that a randomly chosen customer was satisfied in both 2016 and 2017?

0.192

In a recent school election at a large school we know that 45% of the students supported candidate X and the other 55% supported candidate Y. Assume everyone has a strong opinion about one candidate or the other. If we select 2 students at random, what is the probability that they both support candidate X? A. 0 B. 0.2025 C. 0.6975 D. 0.90

B. 0.2025

In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played? A. 0.50 B. 0.25 C. 0.20 D. 0.125

B. 0.25

In a certain liberal arts college with about 10,000 students, 40% are males. If two students from this college are selected at random, what is the probability that they are of the same gender? A. 0.96 B. 0.52 C. 0.48 D. 0.36 E. 0.16

B. 0.52

A six-sided cube is rolled. What is the probability that the number is odd or less than 4? Event A: Numbers on a six-sided cube are odd: 1, 3, 5 Event B: Numbers on a six sided cube are less than 4: 1, 2, 3 A. 1/2 B. 2/3 C. 5/6 D. 1

B. 2/3

Buffy and William decide to play 3 card games together. Let B represent a winning game for Buffy and W represent a winning game for William. Define the even A as "Buffy wins at least one game". What are all the possible outcomes for this event?

BBB, BBW, BWB, BWW, WBB, WBW, WWB

A couple decides to have 2 children. What is the probability that the children are of the same gender? A .25 B .33 C .5 D .75

C .5

A person must enter a password to see their online banking account. They will attempt passwords until they are successful, however they cannot try more than 3 times or they will be locked out of the system. S stands for a successful attempt and F stands for a failed attempt. What is the sample space? A {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF} B {S, FS, FFS} C {S, FS, FFS, FFF} D {S, SS, SSS} E {S, SF, SSF, SSS}

C {S, FS, FFS, FFF}

Let A and B be two disjoint events such that P(A) = 0.30 and P(B) = 0.50. What is P(A and B)? A. 0.65 B. 0.15 C. 0 D. 0.80

C. 0

An engineering school reports that 55% of its students were male (M), 40% of its students were between the ages of 18 and 20 (A), and that 25% were both male and between the ages of 18 and 20. What is the probability of a random student being a female who is not between the ages of 18 and 20? A. 0.27 B. 0.25 C. 0.30 D. 0.45

C. 0.30

The CSU system reported the following probabilities for their student body in 2013. The probability of their student being a male between 17 and 19 is P(A) = 0.11. The probability of their student being a female between 20 and 24, P(B) = 0.30. What is P(A and B) given that year? A. 0.033 B. 0.410 C. 0.377 D. 0

D. 0

The following probabilities are based on data collected from U.S. adults during the National Health Interview Survey 2005-2007. Individuals are placed into a weight category based on weight, height, gender and age. Underweight: 0.019 Healthy Weight: 0.377 Over Weight: 0.35 Obese: 0.254 Based on this data, what is the probability that a randomly selected U.S. adult weighs more than the healthy weight range? A. 0.0889 B. 0.35 C. 0.254 D. 0.604

D. 0.604

For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of 0.99 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. What is the probability that when a theft occurs, at least one of the four systems will detect it? A. (0.99) 4 B. (0.01) 4 C. 1−(0.99)4 D. 1−(0.01)4

D. 1−(0.01)4

For safety reasons, three different alarm systems were installed on the property of a famous movie star. Each of the three systems detects when a trespass occurs with a probability of 0.98 independently of the others. The movie star, obviously, is interested in the probability that when a trespass occurs, at least one of the three systems will detect it. What is the probability that when a trespass occurs, at least one of the systems will detect it? A. (0.98) 3 B. (0.02) 3 C. 1−(0.98)3 D. 1−(0.02)3 E. 3 * (0.98) 1 (0.02) 2

D. 1−(0.02)3

In a recent school election at a large school we know that 45% of the students supported candidate X and the other 55% supported candidate Y. Assume everyone has a strong opinion about one candidate or the other. If we select 2 students at random what is the probability that they both supported the same candidate? A. 0.2025 B. 0.2475 C. 0.3025 D. 0.4950 E. 0.5050

E. 0.5050

A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely? (i) HTHTHTHTHTHT (ii) HTTHHTTHTHHT (iii) HHHHHHHHHHHH (iv) TTTHTHHHHTHH A. (i) because there are an equal number of heads and tails. B. (ii) because there are an equal number of heads and tails but in a random order C. (iii) because heads are just as likely as tails D. (iv) because you won't necessarily get the same number of heads and tails with a fair coin E. They are all equally likely.

E. They are all equally likely.

A fair die is rolled 12 times. Consider the following four possible outcomes: (i) 526321416534 (ii) 112233445566 (iii) 666666666666 (iv) 154351244645 Which of the following is the most likely outcome: (i), (ii), (iii), (iv)? A. (i) because number of die outcomes (1, 2, 3, 4, 5, 6) is equal but in a random order. B. (ii) because the number of die outcomes (1, 2, 3, 4, 5, 6) is equal. C. (iii) because the number 6 is just as likely as any other number on a die. D. (iv) because you won't necessarily get the same number of of die outcomes (1, 2, 3, 4, 5, 6) with a fair die. E. They are all equally likely.

E. They are all equally likely.

__________ methods of determining probability use a series of trials to produce outcomes that could not be predicted in advance.

Empirical

Probability is the __________ that an event will occur.

Likelihood

When P(A) = 0, the event will __________ occur.

Never

The complement of an event A is notated as P(__________).

Not A

Relative Frequency of Event A=

Number of times A occurred/total number of repetitions

What values do we need to use relative frequency concept to estimate probability?

Number of times A occurred/total number of repetitions

To solve for P(A or B), we subtract __________ from P(A) + P(B).

P(A and B)

If two events are disjoint, P(A or B) = __________ + P(B).

P(A)

Rule 3: The Complement Rule

P(not A) = 1 - P(A); that is, the probability that an event does not occur is 1 minus the probability that it does occur. The chance something doesn't occur plus the chance it does occur is always 1.

When choosing appropriate scales for your research, these two characteristics can have a profound impact on the quality of the data you obtain?

Reliability & Validity

We call the possible outcomes of a random experiment the __________.

Sample Space

Rule 4: The Addition Rule for Disjoint Events

The Addition Rule for Disjoint Events: If A and B are disjoint events, then P(A or B) = P(A) + P(B). If two things never happen together, the probability of either is the sum of their probabilities.

Which of the following is easier to code: a closed question or an open-ended question? closed or open

closed

What are the three main types of validity discussed in Part One of Pallant?

content, criterion, and construct