Ch 4 Intro to Prob
When rolling a pair of dice and summing the two values rolled, which of the following are exhaustive events?
- A sum of 6 or more and a sum of 8 or less - An even number and an odd number - A sum of 7 or more and a sum of 6 or less
Which method can be used to help implement the total probability rule
a probability table
The intersection of events A and B, denoted A∩B contains
all outcomes that are in A and B
A subset of the sample space is called a/an ______________
event
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of
event B
A trial, or process, that produces several possible outcomes is referred to as an_______
experiment
The probability of randomly selecting a "spade" from a deck of cards is
0.25
Dimitri is the coach of the high school mathletes team. There are 8 mathletes, but only 5 may represent the school at the upcoming math tournament. Dimitri can choose 5 mathletes from the 8 eligible mathletes in ________________ ways.
56
If an experiment is selecting a card from a deck of cards, then the sample space is
All the cards in the deck
The conditional probability of A given B is calculated by diving the intersection of A and B by the probability of
B
Which of the following BEST represents an empirical probability?
Based on past data, a manager believes there is a 70% chance of retaining an employee for at least one year
When updating a prior probability based on new information, which of the following methodologies is MOST useful?
Bayes' Theorem
A country club has 50 members out of a total of 400 members who play neither tennis nor golf. The value 50 should be inserted into the contingency table in the cell with the letter ____________
C
For hotels in NYC, a travel web site wants to provide information comparing hotel costs (high,average,low) versus the quality ranking of the hotel (excellent, good,fair,bad). A useful way to summarize this data is to construct a
Contingency table
Using the multiplication rule, the probability that event A and event B both occur is computed by multiplying the conditional probability of event A given event B by the probability of
Event B occurs first. Then A happens second given that B has already occurred.
If A and B are independent events, then
P(A)=P(A|B)
The complement rule with respect to event A is
P(A^(C)) = 1 - P(A)
For two events A and B, the multiplication rule is
P(A∩B)= P(A | B) * P(B)
Assume the sample space S={win,loss}. Select which fulfills the requirements of the definition of probability.
P({win})=0.8, P({loss})=0.2
The ________ formula is used to determine the number of ways to arrange (x) objects from a group of (n) objects where the order of the objects matters.
Permutation
Which of the following is an example of a conditional probability?
The probability that Lisa purchases groceries, given that Neil has already purchased groceries
True or false: A resident who lives on the west side is more likely to get a pass than a resident who lives on the east side.
True P(Pass|West) = (0.45)/(0.55) = 0.82 while P(Pass|East) = (0.30)/(0.45) = 0.67
A numerical value that measures the likelihood of an uncertain event is a ________?
probability
A softball coach believes that Laurie has a 0.5 probability of getting a hit against a particular pitcher that Laurie has never batted against before. This type of probability is BEST characterized as a(n)
subjective probability
If two events are independent, then the probability that both events occur equals
the product of the individual probabilities
In order to convert a contingency table into a joint probability table, the frequency of each cell is divided by the
total number of outcomes in the sample space
To calculate the probability of the union of two mutually exclusive events A and B
we add the probability of A to the probability of B
The manufacturer of liquid laundry detergent has a 0.02 probability that the detergent bottles will be improperly filled. There is a 0.03 probability that the label on the bottle will not be affixed properly. If the events of bottle fill and affixing the label are independent, then the probability of a bottle being filled improperly and having an improperly affixed label is
0.0006 Since the events are independent, we calculate 0.02 x 0.03 = 0.006
The probability that Anthony is on time for work is 0.90. The probability that Anthony takes the train to work is 0.80. Given that Anthony takes the train to work, the probability that he is on time is 0.95. The probability that Anthony is on time for work and takes the train is
0.76 P(on time ∩ train) = P(on time | train) x P(train) = 0.95 x 0.80 = 0.76
The odds against a horse winning a race were set at 7 to 1. The probability of that horse not winning the race is
0.875
In a particular industry, it is known that 82% of companies ship their products by truck and 47% of companies ship their product by rail. Forty percent of companies ship by truck and rail. The probability that a company ships by truck or rail is
0.890.82 + 0.47 - 0.40 = 0.89
Mathematically calculate 5!
120
Mike is placing a bet on an upcoming horse race in which seven horses are running. Mike places a trifecta bet that wins only if he correctly picks the first, second, and third place horses, in order. Mike can select the placing order for his bet in _________ ways
210
A festival has become so popular that is must limit the number of tickets it issues. People who hope to attend the festival send in a request for tickets, and requests are filled by random selection. Only 21% of the ticket requests are fulfilled. The odds that a random applicant does not receive a ticket are
3.76 to 1
