STATS Chapter 5
Probabilities are always numbers between and including what numbers?
0 and 1
Which of the following is the probability that something in the sample space will occur?
1 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.
If the probability that it will rain tomorrow is 0.30, the probability that it will not rain tomorrow is what?
1- .30 =0.70
If E represents any event and E^c represents the complement of E, then P(E^c)=__________.
1-P(E) The probability of the complement of an event is one minus the probability of the event itself. Since either the event or the complement must occur, together their probabilities must add to one.
A(n) _______ is any collection of outcomes from a probability experiment.
An event is any collection of outcomes from a probability experiment. Remember that an event is considered "simple" if it only contains one outcome.
In statistics, what is true of randomness?
randomness is hard to achieve without help from a computer or some other randomizing device, such as a random number table.
A person was trying to figure out the probability of getting two heads when flipping two coins. He flipped two coins 10 times, and in 2 of these 10 times, both coins landed heads. On the basis of this outcome, he claims that the probability of two heads is 2/10, or 20%. Is this an example of an empirical probability or a theoretical probability? Explain.
This is an example of empirical probability because it is based on an experiment. Empirical probabilities are short-run relative frequencies based on an experiment.
A friend flips a coin 30 times and says that the probability of getting a head is 60% because he got eighteen heads. Is the friend referring to an empirical probability or a theoretical probability? Explain.
This is an example of empirical probability because it is based on an experiment. Empirical probability changes with every experiment. The larger the number of repetitions, the closer together these probabilities are likely to be.
A Monopoly player claims that the probability of getting a 4 when rolling a six-sided die is 1/6 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.
This is an example of theoretical probability because it is not based on an experiment.
A magician claims that he has a fair coin—"fair" because both sides, heads and tails, are equally likely to land face up when the coin is flipped. She tells you that if you flip the coin three times, the probability of getting three heads is 1/8. Is this an example of a theoretical probability or an empirical probability? Explain.
This is an example of theoretical probability because it is not based on an experiment. Theoretical probability is the relative frequency at which an event happens after infinitely many repetitions. This value never changes.
Probabilities that are based on short-run relative frequencies are called what?
Empirical probabilities Probabilities that are based on short-run relative frequencies are called empirical probabilities. If a coin is tossed 10 times and 6 resutls are heads, the empirical probability of getting heads is 6/10=0.6,or 60%.
When events A and B are said to be independent, what does that mean?
Knowledge that event B occurred does not change the probability of event A occurring.
If events A and B are independent, what must be done to find the probability of event A AND B?
Multiply the probability of A and the probability of B.
When two events have no outcomes in common, they are called what?
Mutually exclusive
Experiments used to produce empirical probabilities are called what?
Simulations Experiments used to produce empirical probabilities are called simulations, because the investigators hope that these experiments simulate the situation they are examining.
Which of the following statements correctly describes the complement of event E?
The complement of event E is the set of outcomes which are in the sample space but not in event E. The complement of an event is the opposite of the event. If you know the probability of an event, you can find the probability of its complement by subtracting the probability of the event from 1.
Given the event "a die lands with a 6 on top", which of the following is the complement of this event?
The die lands with a 1, 2, 3, 4, or 5 on top
The _______ of a probability experiment is the collection of all possible outcomes.
The sample space is the collection of all possible outcomes of an experiment. The sample space is often denoted by "S."
The sample space of a random experiment is what?
The set of all possible and equally likely outcomes of the experiment 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.