MATH 221 - Chapter 5
In statistics, what is true of randomness? A. Randomness is hard to achieve without help from a computer or some other randomizing device. B. Randomness can be achieved by writing a sequence with no structure. C. Randomness means having no apparent pattern. D. Randomness should be avoided because it can lead to incorrect answers.
A. Randomness is hard to achieve without help from a computer or some other randomizing device.
A friend flips a coin 40 times and says that the probability of getting a head is 40% because he got sixteen heads. Is the friend referring to an empirical probability or a theoretical probability? Explain. A. This is an example of empirical probability because it is based on the relative frequency at which an event happens after infinitely many repetitions. B. This is an example of theoretical probability because it is not based on an experiment. C. This is an example of empirical probability because it is based on an experiment. D. This is an example of theoretical probability because it is based on an experiment.
C. This is an example of empirical probability because it is based on an experiment.
Probabilities that are based on short-run relative frequencies are called what? Theoretical probabilities Practical probabilities Pseudo probabilities Empirical probabilities
Empirical probabilities Probabilities that are based on short-run relative frequencies are called empirical probabilities. If a coin is tossed 10 times and 6 results are heads, the empirical probability of getting heads is six tenths =0.6, or 60%.
Experiments used to produce empirical probabilities are called what? Frequencies Simulations Theories Randomizations
Simulations Experiments used to produce empirical probabilities are called simulations, because the investigators hope that these experiments simulate the situation they are examining.
Statistics and probability use the "inclusive OR". This means that referring to outcomes A OR B is referring to what? A. Outcomes that are only in A, only in B, or in both B. Outcomes that are only in B C. Outcomes that are in both A and B D. Outcomes that are only in A
Outcomes that are in A OR B are outcomes that are only in A, only in B, or in both.
Probabilities are always numbers between and including what numbers? 0 and 1 0.01 and 1.0 minus −1 and 1 1 and 100
answer: 0 and 1 Probabilities are always numbers between and including 0 and 1. If the probability of an event happening is 0, then that event never happens. If the probability of an event happening is 1, then that event always happens.
If the probability that it will rain tomorrow is 0.30, the probability that it will not rain tomorrow is what? A. −0.30 B. 0.30 C. 0.70 D. Impossible to determine from the given information
answer: 0.70 The probability that an event does not occur is 1 minus the probability that the event will occur. The probability that it will not rain tomorrow is then 1 − 0.30 = 0.70.
Which of the following is the probability that something in the sample space will occur? A. 0 B. 1 C. 0.50 D. Impossible to determine from the given information
answer: 1 note: The sample space is the set of all possible and equally likely outcomes of the experiment. Because it contains all possible outcomes, the probability that something in the sample space will occur is 1.
Given the event "a die lands with a 6 on top", which of the following is the complement of this event? A.The die lands with a 6 on the bottom B.The die lands with a 3 on the top C.The number of times the die lands with a 6 on top in n throws of the die D.The die lands with a 1, 2, 3, 4, or 5 on top
answer: A The complement is all the ways the die can land with a number that is not a 6 on top. This happens when the die lands with a 1, 2, 3, 4, or 5 on top.
The sample space of a random experiment is what? A. The set of all possible outcomes of the experiment B. The set of all possible and equally likely outcomes of the experiment C. Events that have no outcomes in common D. Any collection of outcomes of the experiment
answer: B note: The sample space of a random experiment is the set of all possible and equally likely outcomes of the experiment. It is often represented with the letter S.
When two events have no outcomes in common, they are called what? Complementary Conditional Mutually exclusive A sample space
answer: Mutually exclusive When two events have no outcomes in common, they are called mutually exclusive. Rolling a 5 on a six-sided die and rolling a 3 on a six-sided die are mutually exclusive events.
Because they are generated by a seed value that starts the random sequence, computer-generated random numbers are sometimes called what? Pseudo-random numbers Arbitrary random numbers Prime random numbers Empirical random numbers
answer: Pseudo-random numbers Computer-generated random numbers are sometimes called pseudo-random numbers. If a researcher inputs the same seed number, that researcher will always see the same sequence of pseudo-random numbers.
A Monopoly player claims that the probability of getting a 4 when rolling a six-sided die is one-sixth because the die is equally likely to land on any of the six sides. Is this an example of a theoretical probability or an empirical probability? Explain. A. This is an example of theoretical probability because it is based on an experiment. B. This is an example of empirical probability because it is based on an experiment. C. This is an example of theoretical probability because it is not based on an experiment. D. This is an example of empirical probability because it is based on the relative frequency at which an event happens after infinitely many repetitions.
note: Theoretical probability is the relative frequency at which an event happens after infinitely many repetitions. This value never changes.
