PROBABILITY & STATISTICS
#2QUESTIONS & ANSWERS(RATED
A+)
Flipping a fair coin is said to randomly generate heads and tails with equal
probability. Explain what random means in this context. - ANSWERIn the long run, a
fair coin will generate 50% heads and 50% tails, approximately. But for each flip, the
outcome cannot be predicted.
A friend says "I flipped five heads in a row! The next one has to be tails!" Explain
why this thinking is incorrect. - ANSWERThere is no law of averages for the short
run. The first five flips do not affect the sixth flip.
In a dresser are ten blue shirts, nine red shirts, and six black shirts.
A. What is the probability of randomly selecting a red shirt?
B. What is the probability that a randomly selected shirt is not black? - ANSWERA.
9/25 = 0.36
B. 19/25 = 0.76
A recent study conducted by a health statistics center found that 23% of households
in a certain country had no landline service. This raises concerns about the accuracy
of certain surveys, as they depend on random-digit dialing to households via
landlines. Pick four households from this country at random. Complete parts a)
through c) below
A. What is the probability that all four of them have a landline?
B. What is the probability that at least one of them does not have a landline?
C. What is the probability that at least one of them does have a landline? -
ANSWERA. 1-0.23 = 0.77
(0.77)^4 = 0.352
B. 1-0.352 = 0.648
C. (0.23)^4 = 0.003
1-0.003 = 0.997
A casino claims that its roulette wheel is truly random. What should that claim mean?
- ANSWEREvery number is equally likely to occur.
Comment on the quotation below from a climatologist.
"What I think is our best determination is it will be a colder than normal winter. I'm
basing that on a couple of different things. First, in look at the past few winters, there
, has been a lack of really cold weather. Even though we are not supposed to use the
law of averages, we are due. " - ANSWERThere is no "law of Averages." She would
be wrong to think they are "due" for a harsh winter.
Suppose that 55% of families living in a certain country own a laptop and 25% own a
desktop computer. The Addition Rule might suggest, then, that 80% of families own
either a laptop or a desktop computer. What's wrong with that reasoning? -
ANSWERA family may own both a laptop and a desktop computer. The events are
not disjoint, so the Addition Rule does not apply.
The property which states that for independent trials, as the number of trials
increases, the long run relative frequency of an outcome gets closer the the true
probability is called the __________. - ANSWERlaw of large numbers
Every morning, my neighbor goes out walking. I observe that 20% of the time she
walks with her beagle, 70% of the time she walks with her golden retriever, and 30%
of the time she walks alone. If these events are all disjoint, is this an example of a
valid probability distributions? - ANSWERThis is not a valid probability distribution
You wake up from a nightmare in which you've completely forgotten about the final
exam in your stats class. Since you haven't studied, you estimate that there is an
80% chance of answering any individual problem correctly. Determine the chance
that you answer a problem incorrectly. - ANSWER100%-80% = 20%
You wake up from a nightmare in which you've completely forgotten about the final
exam in your stats class. Since you haven't studied, you estimate that there is an
80% chance of answering any individual problem correctly. The test is 5 questions
long. If you wanted to find the probability you answer all the questions incorrectly,
what could you do? - ANSWER0.2*0.2*0.2*0.2*0.2
Suppose that 21% of people have a dog, 18% of people have a cat, and 6% of
people own both. What is the probability that someone owns a dog or a cat? -
ANSWER0.21+0.18-.06 = 0.33
A student figures that he has a 13% chance of being let out of class late. If he leaves
class late, there is a 16% chance that he will miss his train. What is the probability
that he gets out of class late and misses the train? - ANSWER0.13*0.16 = 0.0208
rounded to 0.021
Every morning, my neighbor goes out walking. I observe that 20% of the time she
walks with her beagle, 70% of the time she walks with her golden retriever, and 30%
of the time she walks alone. Can the two events (walk with beagle) and (walk with
golden retriever) be disjoint? - ANSWERNo
A standardized value is a value found by which of the following? -
ANSWERSubtracting the mean from the value and then dividing the result by the
standard deviation of the dataset
Which of the following statement is TRUE about a z-score? - ANSWERA. Z-scores
standardize a dataset.
#2QUESTIONS & ANSWERS(RATED
A+)
Flipping a fair coin is said to randomly generate heads and tails with equal
probability. Explain what random means in this context. - ANSWERIn the long run, a
fair coin will generate 50% heads and 50% tails, approximately. But for each flip, the
outcome cannot be predicted.
A friend says "I flipped five heads in a row! The next one has to be tails!" Explain
why this thinking is incorrect. - ANSWERThere is no law of averages for the short
run. The first five flips do not affect the sixth flip.
In a dresser are ten blue shirts, nine red shirts, and six black shirts.
A. What is the probability of randomly selecting a red shirt?
B. What is the probability that a randomly selected shirt is not black? - ANSWERA.
9/25 = 0.36
B. 19/25 = 0.76
A recent study conducted by a health statistics center found that 23% of households
in a certain country had no landline service. This raises concerns about the accuracy
of certain surveys, as they depend on random-digit dialing to households via
landlines. Pick four households from this country at random. Complete parts a)
through c) below
A. What is the probability that all four of them have a landline?
B. What is the probability that at least one of them does not have a landline?
C. What is the probability that at least one of them does have a landline? -
ANSWERA. 1-0.23 = 0.77
(0.77)^4 = 0.352
B. 1-0.352 = 0.648
C. (0.23)^4 = 0.003
1-0.003 = 0.997
A casino claims that its roulette wheel is truly random. What should that claim mean?
- ANSWEREvery number is equally likely to occur.
Comment on the quotation below from a climatologist.
"What I think is our best determination is it will be a colder than normal winter. I'm
basing that on a couple of different things. First, in look at the past few winters, there
, has been a lack of really cold weather. Even though we are not supposed to use the
law of averages, we are due. " - ANSWERThere is no "law of Averages." She would
be wrong to think they are "due" for a harsh winter.
Suppose that 55% of families living in a certain country own a laptop and 25% own a
desktop computer. The Addition Rule might suggest, then, that 80% of families own
either a laptop or a desktop computer. What's wrong with that reasoning? -
ANSWERA family may own both a laptop and a desktop computer. The events are
not disjoint, so the Addition Rule does not apply.
The property which states that for independent trials, as the number of trials
increases, the long run relative frequency of an outcome gets closer the the true
probability is called the __________. - ANSWERlaw of large numbers
Every morning, my neighbor goes out walking. I observe that 20% of the time she
walks with her beagle, 70% of the time she walks with her golden retriever, and 30%
of the time she walks alone. If these events are all disjoint, is this an example of a
valid probability distributions? - ANSWERThis is not a valid probability distribution
You wake up from a nightmare in which you've completely forgotten about the final
exam in your stats class. Since you haven't studied, you estimate that there is an
80% chance of answering any individual problem correctly. Determine the chance
that you answer a problem incorrectly. - ANSWER100%-80% = 20%
You wake up from a nightmare in which you've completely forgotten about the final
exam in your stats class. Since you haven't studied, you estimate that there is an
80% chance of answering any individual problem correctly. The test is 5 questions
long. If you wanted to find the probability you answer all the questions incorrectly,
what could you do? - ANSWER0.2*0.2*0.2*0.2*0.2
Suppose that 21% of people have a dog, 18% of people have a cat, and 6% of
people own both. What is the probability that someone owns a dog or a cat? -
ANSWER0.21+0.18-.06 = 0.33
A student figures that he has a 13% chance of being let out of class late. If he leaves
class late, there is a 16% chance that he will miss his train. What is the probability
that he gets out of class late and misses the train? - ANSWER0.13*0.16 = 0.0208
rounded to 0.021
Every morning, my neighbor goes out walking. I observe that 20% of the time she
walks with her beagle, 70% of the time she walks with her golden retriever, and 30%
of the time she walks alone. Can the two events (walk with beagle) and (walk with
golden retriever) be disjoint? - ANSWERNo
A standardized value is a value found by which of the following? -
ANSWERSubtracting the mean from the value and then dividing the result by the
standard deviation of the dataset
Which of the following statement is TRUE about a z-score? - ANSWERA. Z-scores
standardize a dataset.
