chapter4-5 Flashcards


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1

If E and F are not disjoint​ events, then​ P(E or ​F)equals=

P(E) + P(F) - P(E and F)

2

Suppose an experiment consists of rolling a fair die ten times and recording the number of sevens obtained. If event E is defined as getting at least one​ 7, how would you describe the complement of​E?

The complement of event E is the event that no sevens are obtained.

3

Three cards are drawn without replacement from a standard​ deck, and the number of kings is noted. Does this constitute a binomial​ experiment? Why or why​ not?

​No, because the probability of getting a king is not the same for each of the three draws.

4

any collection of outcomes from a probability experiment.

event

5

The probability of obtaining x successes in n independent trials of a binomial experiment is given by ​P(x)equals=Subscript n Baseline Upper C Subscript x Baseline p Superscript x Baseline left parenthesis 1 minus p right parenthesis Superscript n minus xnCxpx(1−p)n−x​, where p is the probability of success. *What does the n−x represent in the​formula?

the number of failures

6

Suppose a fair die is rolled ten times and the result is recorded each time. Does this constitute a binomial​ experiment?

​No, because there are more than two outcomes for each trial.

7

Three cards are drawn with replacement from a standard​ deck, and the number of kings is noted. Does this constitute a binomial​ experiment?

​Yes, because there are three independent draws. For each draw there are two outcomes​(king and not​ king) and a constant probability of getting a king.

8

random variable has either a finite or countable number of values

discrete

9

If E represents any event and Upper E Superscript cEc represents the complement of​ E, then Upper P left parenthesis Upper E Superscript c right parenthesis equalsPEc=

1-P(E)

10

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that at least 30 adults have at least a​ bachelor's degree?

P(x greater than or equal to 30)

11

Use symbols to describe the event that a college student is female or has financial aid.

AUB

12

Two events E and F are​ __________ if the occurrence of event E in a probability experiment does not affect the probability of event F.

independent

13

Consider the binomial probability distribution function Upper P left parenthesis x right parenthesis equals StartFraction 25 exclamation mark Over x exclamation mark left parenthesis 25 minus x right parenthesis exclamation mark EndFraction 0.6 Superscript x Baseline 0.4 Superscript 25 minus xP(x)=25!x!(25−x)!0.6x0.425−x. What is the probability of​ success?

0.6

14

The Addition Rule​ P(E or ​F)=​P(E)+​P(F) applies only to which type of​ events?

disjoint

15

Determine whether the distribution is a discrete probability distribution

​No, because the probabilities do not sum to 1.

16

The notation​ __________ is used for the binomial random variable which counts the number of successes in n independent trials of an experiment.

x

17

is a numerical measure of the outcome of a probability experiment

random variable

18

of a probability experiment is the collection of all possible outcomes

sample space

19

is used for the number of trials in a binomial experiment.

n

20

Suppose that in a certain​ community, the probability of a randomly selected individual having red hair is 0.08 and the probability of a randomly selected individual being​ left-handed is 0.15. What additional information would be needed to find the probability of randomly selecting an individual in this community who has red hair or is​ left-handed?

We would need to know the percentage of individuals in the community who have red hair and are​ left-handed.

21

Use symbols to describe the event that a college student is female and has financial aid.

A (upsidown U) B

22

If a sample of 100 people is chosen from a town of​ 100,000 people without​ replacement, is it reasonable to assume that events are​ independent

Yes. Because the sample size is less than​ 5% of the population​ size, it is reasonable to treat the events as independent.

23

Suppose two events E and F are disjoint. What is​ P(E and​ F)?

0

24

Explain how to find the mean of a discrete random variable.

To find the mean of a random​ variable, multiply each value of the random variable by its probability and then add those products.

25

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. Which of the following probability statements indicates the probability that fewer than 30 adults have at least a​ bachelor's degree?

P(x less than 30)

26

Identify the requirements for a discrete probability distribution.

The sum of the probabilities must equal one. Each probability must be between zero and one inclusive.

27

What does it mean to say that the trials in a binomial experiment are independent of each​ other?

The outcome of one trial does not affect the outcomes of the other trials.

28

What is the mean of a probability​ distribution?

The mean is the expected value of the random variable

29

How many trials are in the​ experiment?

25

30

Which of the following statements is not true about binomial probability​ distributions?

As the probability of success​ increases, the probability distribution for a binomial variable becomes bell shaped.

31

Suppose you are trying to calculate the probability that someone passes statistics on the first attempt given that they received an A in their previous math course. Which probability do you divide by when using conditional probability​ rule?

the probability that someone received an A in their previous math course

32

When a constant is added​ (or subtracted) to each value of a random​ variable, which measures do not increase​ (or decrease) by that same​ amount?

measures of spread

33

The probability that a randomly selected adult in a particular community is a smoker is​ 20%. The probability that a randomly selected adult in the community is a​ smoker, given that the adult earns more than​ $75,000 per​ year, is​ 10%. Are the events​ "is a​ smoker" and​ "earns more than​ $75,000 per​year" independent? Explain.

​No, because the probability of smoking is different for people who earn over​ $75,000 per​year, the events are not independent.

34

How would you find the probability that a man in this age category does NOT die of cancer during the course of the​ year?

1-0.003

35

Which of the following is not a valid explanation of the Law of Large​ Numbers

These statements are all valid

36

If two events E and F are​ independent, then​ P(E and ​F)=

P(E) x P(F)

37

is used for the probability of failure on any trial in a binomial experiment.

1-p

38

If two events E and F are not​ independent, then​ P(E and ​F)equals=

P(E) x P(F/E)

39

Cards are drawn with replacement from a standard deck until a king is drawn. Does this constitute a binomial​ experiment

No, because there is not a fixed number of trials.

40

When considering events resulting from a single​ trial, if one event is the complement of another​event, must those two events be​ disjoint

Yes; There is no overlap between an event occurring and the event not occurring. They are completely separate and disjoint.

41

Suppose you want to know how likely it is that a student graduates with a​ Bachelor's degree in 4 years if they were in the top​ 10% of their high school graduating class. Which of the following probabilities will answer your​ question

​P(earn BS​ degree|top 10%)

42

is used for the probability of sucess on any trial in a binomial experiment

p

43

Explain how to read the notation​ P(E|F).

the probability of E given F

44

Which terms are used to describe events that have no outcomes in​ common

disjoint or mutually exclusive

45

The binomial probability distribution is a ​ __________ probability distribution that describes probabilities for experiments in which there are two​ __________ outcomes.

discrete

mutually ecxlusive

46

Use symbols to describe the event that a college student is female given that​ he/she has financial aid.

A|B

47

random variable has infinitely many values which can be plotted on a number line in an uninterrupted fashion.

continuous

48

Describe the event C|A in words.

A college student finishes​ his/her undergraduate degree in four years given that the student is female.

49

Suppose that a binomial random variable X is counting the number of patients with cancer at a particular hospital. How will​ "success" be defined in this​ situation?

Success would be defined as selecting a patient at the hospital who has cancer.

50

Describe how the value of n affects the shape of the binomial probability histogram.

As n​ increases, the binomial distribution becomes more​ bell-shaped.

51

How would you find the probability that no men out of​ 1,000 of this age will die of cancer during the course of the​ year?

(0.997)^1000

52

How would you find the probability that at least 1 man out of​ 1,000 of this age will die of cancer during the course of the​ year?

1-(0.997)^1000

53

Which of the following is not a criterion for the binomial​ distribution?

The trials must be dependent.

54

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using the binomial probability​ formula, which of the following is the most efficient way to calculate the probability that at most 98 adults have a​ bachelor's degree, ​P(xless than or equals≤​98)?

1−​P(x=​99)−​P(x=​100)

55

Use symbols to describe the event that a college student finishes​ his/her undergraduate degree in four years if​ she/he does not have financial aid

C|B'