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Key Concepts:
Terms in this set (117)
What are mutually exclusive events?
Events in which neither event is dependent upon the other
A number is chosen at random from the first 100 positive integers. Find the probability that the number chosen is prime.
1/4
A number is chosen at random from the first 100 positive integers. Find the probability that the number is divisible by 5.
1/5
A number is chosen at random from the first 100 positive integers. Find the probability that the number is a multiple of 7.
7/50
A number is chosen at random from the first 100 positive integers. Find the probability that the number is either even or a perfect square.
11/20
A number is chosen at random from the first 100 positive integers. Find the probability that the number is not divisible by 10 or 3.
3/5
A certain class of 160 students has 40 honor students and 60 athletes. Eighty students in the class do not participate in sports and are not honor students. If a student is selected at random to represent the class, what is the probability that he is both an honor student and an athlete?
1/8
A number is selected from the set {1, 2, 3, 5, 15, 21, 29, 38, 500}. If equal elemental probabilities are assigned, what is the probability that the number chosen is either less than 29 or odd?
7/9
Independent events are ______.
events in which the probability of A has no effect on the probability of B
A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. What is the probability that the student chosen is an honor student given that he is an athlete?
I believe 1/2
A class of 160 students contains 40 honor students, 60 athletes, and 80 who are neither athletes nor honor students. From the entire group a student is chosen at random. What is the probability that the student chosen is an athlete given that he is an honor student?
1/2 or 1/4
A job applicant estimates that his chance of passing a qualifying examination is , and his chance of being appointed if he does pass is . What is the probability that he will receive the job?
1/6
At the time of a certain marriage, the probabilities that the man and the woman will both live fifty more years are 0.352 and 0.500, respectively. What is the probability that both will be alive fifty years later?
.0176
A certain city has one chance in two of receiving rain on June 1, one chance in five of receiving rain on July 1, and two chances in three of receiving rain on August 1. What is the probability that the city will receive rain on all of these days?
1/15
A certain city has one chance in two of receiving rain on June 1, one chance in five of receiving rain on July 1, and two chances in three of receiving rain on August 1. What is the probability that the city will receive rain on none of these days?
2/15
`Of one hundred envelopes in a box, one envelope contains a $20 bill, five others each contain a $1 bill, and the rest are empty. Find the probability that on the first two draws, envelopes containing money will be drawn.
1/330
One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are black.
3/8
One bag contains three white marbles and five black marbles, and a second bag contains four white marbles and six black marbles. A person draws one marble from each bag. Find the probability that both marbles are of the same color?
21/40
At a busy street corner, the probability is that one of every hundred jaywalkers will be hit. What is his probability of not being hit if he makes a round trip daily for thirty days?
(0.9801)^30
The order in which conditions are combined does not matter in a _____.
combination
A certain make of car is available in 5 body types, 4 colors, and 3 kinds of upholstery. How many cars would a dealer have to keep in stock to be able to show his complete line to prospective customers?
60
The Greek alphabet contains 24 letters. How many fraternity names with Greek letters can be formed if each fraternity name contains 2 letters and repetition of letters is permitted?
576
The Greek alphabet contains 24 letters. How many fraternity names with Greek letters can be formed if each fraternity name contains 3 letters and repetition of letters is not permitted?
12144
How many two-digit positive integers can be formed from the digits 1, 5, 6, and 8 if no digit is repeated?
12
In how many ways can a judge award first, second, and third places in a contest with 10 entries?
720
In a certain manufacturing plant, the first operation can be done on any one of five machines, the second operation on only one machine, the third operation on any one of six machines, and the fourth operation on either of two machines. Over how many routes can the raw material be processed?
60
An automobile designer is considering three body designs, five hood designs, and three fender designs. How many models would be required to show all possible ways of combining the designs?
45
A man tries to predict the winner of each of twenty football games. Excluding ties, how many different predictions are possible?
2^20
A clothing store stocks socks made of either cotton or wool, each in five colors, and each in seven sizes. How many items are needed for a complete assortment?
70
The dial of a combination lock has all 26 letters of the alphabet on it. A combination is formed by dialing 3 different letters in a particular order. If the owner of the lock forgets the combination, how many trials may be needed to open the lock?
15600
From the digits 9, 8, 7, 5, 3, and 1, find the number of positive integers, each consisting of three digits
216
From the digits 9, 8, 7, 5, 3, and 1, find the number of positive integers, each consisting of three different digits.
120
From the digits 9, 8, 7, 5, 3, and 1, find the number of positive even integers each consisting of three digits.
36
From the digits 1, 2, 3, and 4, how many positive integers are less than 100,000? Consider the possibilities for 5-digit, 4-digit, 3-digit, 2-digit, and 1-digit numbers and repetition of digits.
1364
A cellphone/telephone keypad has keys numbered with the digits 0 to 9, inclusive. Each of the keys, except the "1" (one) and "0" (zero) keys, also contains letters. How many different telephone numbers are possible using this keypad, if each "number" consists of two letters followed by five digits, where the first digit is not zero?
576,000,000
Compute the permutation.30 P 3
24,360
How many different positive integers of 2 digits each can be made with the digits 2, 4, 5, and 8, if no digit is repeated in a number?
12
How many positive integers of 3 digits each can be formed with the digits 1, 8, 9, 2, 7, 6, 4, and 3, if no digit is repeated in a number?
336
A chemist has eight test tubes to examine. In how many orders can he do this examination?
40320
What is the general form for permutations when there are two set of items within the group (n) that are the same?
n!/p!q!
In how many different, distinguishable orders can the letters of the word "TENNESSEE" be arranged?
3,780
The ten students in a club are lined up in a row for a group photograph. How many different arrangements are possible if the club includes one set of identical triplets wearing matching clothes?
604,800
An electronic salesperson carries 6 identical amplifier tubes, 5 identical rectifiers, 2 identical condensers, and 4 identical relays. In how many different ways can these parts be arranged in a row?
17!/(6!5!2!4!)
How many permutations can be made of the letters of the word "radar" when taken all at a time?
30
How many permutations can be made of the letters of the following word "proposition" when taken all at a time?
11!/24
How many distinct signals can be made with 8 flags displayed at the same time in a vertical array if 3 flags are white, 2 flags are red, 1 flag is checkered and the rest of the flags are yellow?
1680
How many distinguishable ways can you arrange the letters in the word "MISSISSIPPI"?
34650
The number of ways a group of objects can be arranged around a closed curve is known as ______.
circular permeation
In how many ways can 8 diplomats be seated at a round table?
5040
In how many different ways can 7 children join hands to form a circle if they face the center?
720
In how many ways can 10 adults be seated at a round table?
9!
In how many orders can 4 boys and 4 girls be seated at a round table if the boys and girls alternate?
36
In how many ways can 5 men and 5 women be seated at a round table if the men and women alternate?
576
A wheel for a game is to be made by dividing a circular disk into six equal pie-shaped wedges and numbering them from 1 to 6. In how many ways can this numbering be done?
120
In how many ways can a committee of six be seated at a round table if the chairman and the secretary must sit together?
48
In how many ways can 5 children sit at a round table?
24
In how many ways can 6 people stand in a circle?
120
In _____, the order the variables are chosen in does not matter.
combinations
Find the value of the combination.
7 C 2
21
Find the value of the combination.
5 C 5
1
Find the value of the combination.
13 C 5
1287
Find the value of the combination.
16 C 14
120
Find the value of the combination.
21 C 3
1330
Find the value of the combination.
8 C 6
28
Find the value of the combination.
10 C 0
1
Find the value of the combination.
9 C 4
126
In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible?
56
A farmer buys three cows, two pigs, and ten sheep from a seller who has seven cows, four pigs, and ten sheep. How many choices of animals does he have
210
From a committee consisting of 8 men and 5 women, a subcommittee is formed consisting of 4 men and 3 women. How many different subcommittees are possible?
700
A boy wishes to invite 10 of his friends to his home. How many ways can he invite them as guests?
1023
In how many different ways can 8 letters be placed in a mailbox?
255
A club contains 9 members. In how many ways can the president name a committee if the president is not eligible to be a member of the committee?
255
Which expression can be expanded using the Binomial theorem?
(x^2 - 1)^3
Sally wants to expand (3a + b)^7. Which row of Pascal's triangle should she use?
7
What is the coefficient of the third term in a binomial that is raised to the sixth power?
15
Which of the following is the correct expansion of (3x - y)^2?
9x^2 - 6xy + y^2
Which of the following is the correct expansion of (2x - 5y)2?
4x2 - 20xy + 25y2
What is the coefficient of the second term in a binomial that is raised to the fifth power?
5
How many ways can two flowers be chosen from a set of five?
10
How many ways can two marbles be chosen from a set of six marbles?
15
The logistical process for proving if a proposition involving a positive integer n can be proved to have the following properties, then the proposition is true for all positive integral values of n is known as ______.
mathematical induction
4
E i^2
i-0
30
5
E (2i+1)
i-1
35
4
E [(i-1)^2 + (i+1)^3]
i-1
238
Find the 15th term of the sequence 5, 8, 11, 14, 17...
47
Which of the following is the general term for the sequence?
-m, m, -m, m, . . .?
an = -m(-1)^n - 1
What is the recursive formula for the sequence 3, 12, 48, 192, 768...?
a1 = 3, an = (an - 1)(4)
Indicate a general rule for the nth term of the sequence when a1 = 5 and r=squareroot of 2.
an=(5)(sqre root 2)^n-1
For the geometric sequence where a1 = 3 and r=squre root 2 , find the 10th term of the sequence.
48 sqre root 2
Summations are used to _____.
simplify the addition of large amounts of numbers
5
E 2i+1
i-1
35
7
E i-1
i-1
21
3
E i^3
i-1
36
4
E i^-1
i-1
25/12
5
E 2^i
i-1
62
3
E 2^-i
i-1
7/8
6
E (i-1)^2
i-3
54
3
E i^2 +3i +2
i=1
38
5
E ai
i=1
15a
7
E a +2i
i-1
7a+56
Express the series using sigma notation.
4 + 16 + 64 + 256 + 1,024
5
E 4(4)^n-1
i-1
Find the sum of the arithmetic series.
8
E (1/4)n+1
n-1
17
Find the sum of the geometric series.
4
E 4(1/2)^n-1
n-1
7.5
Express the series using sigma notation.
5 + 8 + 11 + 14 + 17...
inf
E 3n+2
n-1
Express the series using sigma notation.
5 + 15 + 45 + 135 + 405
5
E5(3)^n-1
n-1
Express the series using sigma notation.
2 - 6 + 18 - 54 + 162 ...
inf
E 2(-3)^n-1
n-1
Given an event which may or may not occur ("heads" in a coin toss), a form of statistical analysis describing the possible number of times that event will happen in a series of observations or trials.
binomial distribution
Any one of the number of different ways in which a number of different objects can be arranged about a circle or any other closed curve. The number of circular permutations of n things is (n - 1).
circular permutation
A group of objects in which the order or arrangement is not considered. The formula for combinations is (n/r)= n!/(n-r)!r!
combination
Events equally probable of happening; the probability that each of them will occur is 1/n.
equally likely events
A subset of a sample space
event
If event A and event B have nonzero probabilities in a sample space, and if and only if P A arc B = PA x PB , then events A and B are independent events.
independent events
Events that are determined when P(A arc B) =0.
mutally exclusive events
An arrangement of a group of objects in a definite order. The formula for permutations is nPr= n!/(n-r)!r!
permutation
Likelihood of occurring. . The formula for addition of probabilities is . If , then . The formula for multiplication of probabilities is . The formula for conditional probability is
probablility
The set of all possible outcomes of a random experiment.
sample space
Total of probabilities assigned to all the elements of a sample space; equals 1.
sum of probablities
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