TEST 2
In probability, a(n) ________ is any process that can be repeated in which the results are uncertain.
Experiement
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Guessing the last digit in the price of a TV. Answer: (0,1,2,3,4,5,6,7,8,9)-There are 10 outcomes in the sample space.
If two events are ____if the occurrence of event E in a probability experiment does not affect the probability of event F.
INDEPENDENT
The word OR in probability implies that we use the
ADDITION RULE
The word and in probability implies that we use the ________ rule.
AND
Suppose you toss a coin 100 times and get 58 heads and 42 tails. Based on these results, what is the probability that the next flip results in a tail?
.42
According to a certain country's department of education, 43.1% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care. The probability that a randomly selected 3-year-old is enrolled in day care is
.431
What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible? What is the probability of an event that is impossible?
0
A lottery exists where balls numbered 1 to 23 are placed in an urn. To win, you must match the six balls chosen in the correct order. How many possible outcomes are there for this game?
23nPr6=72681840
Suppose that a local area network requires eleven letters for user names. Lower- and uppercase letters are considered the same. How many user names are possible for the local area network?
26^11
Four members from a 29-person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible?
29nPr4=570024
Assuming that no questions are left unanswered, in how many ways can a five-question true dash false quiz be answered?Assuming that no questions are left unanswered, in how many ways can a five-question true dash false quiz be answere
2^5=32
How many different simple random samples of size 5 can be obtained from a population whose size is 41?
41nCr5=749398
Describe what an unusual event is. Should the same cutoff always be used to identify unusual events? Why or why not?
An event is unusual if it has a low probability of occurring. The same cutoff should not always be used to identify unusual events. Selecting a cutoff is subjective and should take into account the consequences of incorrectly identifying an event as unusual.
How Does the Law of Large Numbers Apply to gambling casinos??
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome. This applies to casinos because they are able to make a profit in the long run because they have a small statistical advantage in each game.
A ___ is an arrangement of r objects chosen from n distinct objects without repetition and without regard to order.
Combination
When two events are disjoint, they are also independent.
FALSE
Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible?
NO
According to a center for disease control, the probability that a randomly selected person has hearing problems is 0.142. The probability that a randomly selected person has vision problems is 0.089. Can we compute the probability of randomly selecting a person who has hearing problems or vision problems by adding these probabilities? Why or why not?
NO because hearing and vision problems are not mutually exclusive. So, some people have both hearing and vision problems. These people would be included twice in the probability.
If events E and F are disjoint and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion.
NO, events E and G are not necessarily disjoint. For example, Eequals{0,1,2}, Fequals{3,4,5}, and Gequals{2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.
If E and F are disjoint events, then P(E or F)=
P(E)+P(F)
If E and F are not disjoint events, then P(E or F)=
P(E)+P(F)-P(E or F)
A ____ is an ordered arrangement of r objects chosen from n distinct objects without repetition.
Permuation
In a combination problem, order is not important.
TRUE
Probability is a measure of the likelihood of a random phenomenon or chance behavior.
TRUE
Describe the difference between classical and empirical probability.
The empirical method obtains an approximate empirical probability of an event by conducting a probability experiment. The classical method of computing probabilities does not require that a probability experiment actually be performed. Rather, it relies on counting techniques, and requires equally likely outcomes.
In a certain card game, the probability that a player is dealt a particular hand is 0.32. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 32 times? Why or why not?
The probability 0.32 means that approximately 32 out of every 100 dealt hands will be that particular hand. No, you will not be dealt this hand exactly 32 times since the probability refers to what is expected in the long-term, not short-term.
Determine why it is not a probability model. Choose the correct answer below.
This is not a probability model because at least one probability is less than 0.
When an event is almost certain to happen, its complement will be an unusual event.
True, the complement would be an unusual event.
Is the table above an example of a probability model?
Yes because the probabilities sum to 1 and they're all greater than or equal to zero and less than or equal to 1.
A salesperson must travel to 11 cities to promote a new marketing campaign. How many different trips are possible if any route between cities is possible?
ll!
The factorial symbol, n!, is defined as n!= and 0!
n(n-1) times....3*2*1 and 1
