1) Decks of Pinochle cards have a total of 48 cards and consist of 8 cards each of nines, tens, jacks, queens, kings, and aces with there being two of each suit of each denomination (for example, there are 2 aces each of diamonds, clubs, hearts, and spades for the total of 8 aces). Suppose that you are dealt a 7-card hand from a deck of Pinochle cards. What is the probability that:
a) you are dealt at most 2clubs?
b) you are dealt exactly 1ten?
2) Suppose that you roll a pair of 14-sided dice (with the sides numbered 1-14) a total of 53 times.
What is the probability that you will get a sum of 27 at leasttwice?
3) As of the second quarter of 2015, Facebook had approximately 1.5 billion users worldwide and asof May 2015, three of the most popular games on Facebook amongst daily active users (#1, 3, and 4 respectively if you are interested) were Candy Crush Saga (often just referred to as Candy Crush), Farmville, and Clash of Clans. Suppose that 7,500 daily Facebook users were asked whether or not they played each of the three games. The survey found that 1,143 played Candy Crush, 1,034 played Farmville, 649 played Clash of Clans, 656 played Candy Crush and Farmville, 269 played Candy Crush and Clash of Clans, 156 played Farmville and Clash of Clans, and 102 played all three.
a) How many users play Candy Crush but do not play Farmville?
b) How many users play exactly one of the three games?
4) Based upon statistical studies it has been found that 4.22% of all households in the United States in 2010 had a combined household income above $250,000. If 14,000 households from 2010 are selected at random, what is the probability that:
a) between 600 and 650 of them (inclusive) had a household income above $250,000?
b) at least 575 of them had a household income above $250,000?
5) Suppose an unfair coin comes up tails 34.7% of the time if it is flipped. If the coin is flipped 14 times, what is the probability that:
a) it comes up heads exactly 8 times?
b) it comes up tails more than 12 times?
6) The weights of full-grown European turtle doves are known to be normally distributed with a mean of 128 grams and a standard deviation of 14.5 grams. What is the probability that a randomly selected turtle dovewill:
a) be at least 110 grams?
b) be less than 100 grams or more than 150 grams?
7) The number of home runs hit by each of the 20 regular first basemen during the 1966 Major League base ball season is given in the following table (regular is being defined as the player that started the most games at first base for each team that season):
|
Player
|
Team
|
HomeRuns
|
|
FelipeAlou
|
ATL
|
31
|
|
ErnieBanks
|
CHN
|
15
|
|
NormCash
|
DET
|
32
|
|
OrlandoCepeda
|
STL
|
17
|
|
DonnClendenon
|
PIT
|
28
|
|
KenHarrelson
|
KC
|
5
|
|
ChuckHarrison
|
HOU
|
9
|
|
EdKranepool
|
NYN
|
16
|
|
WillieMcCovey
|
SF
|
36
|
|
TomMcCraw
|
CHA
|
5
|
|
DonMincher
|
MIN
|
14
|
|
DickNen
|
WAS
|
6
|
|
WesParker
|
LA
|
12
|
|
JoePepitone
|
NYA
|
31
|
|
TonyPerez
|
CIN
|
4
|
|
BoogPowell
|
BAL
|
34
|
|
GeorgeScott
|
BOS
|
27
|
|
NormSiebern
|
CAL
|
5
|
|
BillWhite
|
PHL
|
22
|
|
FredWhitfield
|
CLE
|
27
|
a) Find the range, mean, median, and mode of the dataset
b) What proportion of the data is within 1 standard deviation of the sample mean?
c) Construct a histogram using classes of size 8 and using 0 as the minimum possible value.
8) The Hawaiian alphabet (known as the piapa) was first written by 19thcentury missionaries and consists of 12 letters; the vowels A, E, I, O, and U, and the consonants H, K, L, M, N, P, and W. Assuming that all possible arrangements of these letters could bewords:
a) What is the maximum possible number of 7-letterwords?
b) What is the maximum possible number of 6-letter words in which no letters arerepeated?
c) How many 10-letter words can start with a W, end with a U, and contain noE's?
d) How many distinct arrangements are there of the letters in WAIANAPANAPA?
9) Three marbles are chosen without replacement from a box containing 4 green, 2 red, 1 yellow, and 5 blue marbles. Let X be the number of blue marbleschosen.
a) Find and graph the probability distribution of X.
b) Find the mean of the random variable X.
10) Suppose that you select 2 cards without replacement from a standard deck of 52 playingcards.
a) If the first card that you select is not a seven, what is the probability that the second card that you select is aseven?
b) If the first card that you select is a heart, what is the probability that the second card thatyou select is anine?
11) Suppose that a teacher is going to assign a book report to her class of 27 students. Each student must select one book from an approved reading list and once a book is selected by a student, no other student may select the same book. The reading list consists of a total of 36 books of which 26 are considered classic fiction and the other 10 are considered modern fiction. Assuming that the order in which the books are selected doesn'tmatter:
a) In how many ways can the books be selected so that all of the classic fiction books arepicked?
b) In how many ways can the countries be assigned so that there is at least one modern fiction bookthat is not picked and at least one classic fiction book that is notpicked.
12) A company that produces a particular machine component has 3 factories, one each in Buffalo, Dayton,and Pittsburgh. 28% of the components produced come from the Buffalo factory, 39% of the components come from the Dayton factory, and 33% of the components come from the Pittsburgh factory. It is known that 1.5% of the components from the Buffalo factory, 1.7% of the components from the Dayton factory, and 1.9% of the components from the Pittsburgh factory are defective. Given that a component is selected at random and is found not to be defective, what is the probability that the component was made in Buffalo?