Survey Math: Chapter 11

EX: In order for the company to make a profit of​ $50 per​ policy, it must take in​ _________ than it spends on each policy.

$50 more.

The probability of an event occurring at least once is equal to 1 minus the probability that the event _______.

Does not occur. If the event does not​ occur,then the event did not occur at least once.

T/F: Because the words BET and BEE both contain three​ letters, the number of permutations of the letter in each word is​ 3!, or 6.

False. Since BEE has two repeating​ letters, the number of permutations is 3!/2!1!​, which equals 3.

The order matters in ______.

Permutation.

nPr = ?

n!/(n−r)! (perm)

0! = ?

1.

A company breaks even when its income is ________ to its expenses.

Exactly equal.

Probability that is based on situations in which we observe how frequently an event occurs is called​ ______.

Empirical.

A mathematical way to use probabilities to determine what to expect in various situations over the long run is called ______________.

Expected Value.

T/F: If an event cannot​ occur, its probability is minus−1.

FALSE. "If an event cannot​ occur, its probability is​ 0."

T/F: Probability problems with the word​ "or" involve more than one selection.

FALSE. "Or" problems always involve only one selection. "And" problems have more than one.

T/F: If an experiment is repeated more and more​ times, the theoretical probability of an event tends to get closer to the empirical probability of that event.

FALSE. As an experiment is repeated more and more​ times, the EMPIRICAL probability of that event tends to get closer to the theoretical probability of the event.

T/F: According to a national center for health​ statistics, the lifetime odds in favor of dying from heart disease are 1 to​ 5, so the probability of dying from heart disease is 1/5.

FALSE. If the odds in favor of event E are a to​ b, then the probability is P(E) = a / a + b

T/F: Combination problems involve situations in which the order of the items makes a difference.

FALSE. To make this statement​ true, change​ "makes a​ difference" to​ "does not make a​ difference".

T/F: The probability of A or B can always be found by adding the probability of A and the probability of B.

FALSE. if probabilities of events A and B are not mutually exclusive events then the probability that A or B will occur is determined by adding their individual probabilities and subtracting the probability that A and B occur simultaneously.

The number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. This is called the __________.

Fundamental Counting Principle.

The standard way to find expected value is to ______ each possible outcome by its​ probability, and then ____ these products.

Multiply; add

The theoretical probability of event​ E, denoted by ​ ______, is the​ ______ divided by​ ______.

P(E) ; # of outcomes in event E [n(E)] divided by # of possible outcomes, n(S).

The set of all possible outcomes of an experiment is called the​ _______ of the experiment.

Sample Space.

T/F: If an even is certain to occur, its probability is 1.

TRUE.

T/F: P(B|A) is the probability that event B occurs if the sample space is restricted to the outcomes associated with event A.

TRUE.

T/F: The probability that an event happens at least once can be found by subtracting the probability that the event does not happen from 1.

TRUE.

T/F: The sum of the probabilities of all possible outcomes in an experiment is 1.

TRUE.

T/F: Using the Fundamental Counting​ Principle, if you can choose one item from a group of M items and a second item from a group of N​ items, then the total number of​ two-item choices is M times N.

TRUE.

T/F: Within​ reason, regardless of the United States​ population, we will not run out of telephone numbers as long as we continue to add new digits.

TRUE. Because each additional digit adds to the total number of phone numbers by a power of​ 10, there will always be enough phone numbers.

T/F: Games in gambling casinos are set up so that expected values are negative.

TRUE. Needs to be negative for the casino to make money.

The number of permutations of n​ items, where p items are identical and q items are​ identical, is given by _______.

n!/p!q! (perm)

The number of possible combinations of r objects are taken from n items is _______.

nCr = n!/(n−r)! r! (combo?)

The formula for nCr has the same numerator as the formula for nPr but contains an extra factor of​ _____ in the denominator.

r!