Statistics Homework - need it by tomorrow!

QUESTION 1

It is known that when a particular 4-sided die is rolled, a 1 will come up 30% of the time,
a 2 will come up 20% of the time, a 3 will come up 20% of the time, and a 4 will come
up 30% of the time.  If the die is rolled a total of four times, what is the probability that
it comes up 4 on at least three of the rolls?

A. 0.0272

B. 0.0756

C. 0.0837

D. 0.1080

E. 0.1161

QUESTION 2

In a TV game show, 4 prizes are hidden on a game board that contains 20 spaces.
One prize is worth $10,000, two prizes are worth $5,000 each, and one prize is 
worth $1,000, with the remaining spaces containing no prize.  The show's host
offers a contestant their choice of $1,000 (for not playing) or the opportunity to
slect one space on the game board.  How much greater is the expected value of 
picking a space on the board than not playing the game?

A. $50

B. $100

C. $1,000

D. $4,500

E. The expected value is greater for not playing the game than it is for playing it.

QUESTION 3

An unfair coin comes up heads 53% of the time that it is flipped.  If the coin is flipped
12 times, what is the probability that it comes up heads exactly 6 times?

A. 0.0443

B. 0.1294

C. 0.1330

D. 0.2048

E. 0.2208

QUESTION 4

Suppose that you play a game where you roll a fair standard 6-sided die and based on
the outcome you either win or lose money.  If you roll a 6 you win $20 and if you roll 
anything other than a 6 you lose $3.  If you play this game three times, what is the 
expected value of your winnings?

A. $6

B. $10

C. $15

D. $30

E. None of These

QUESTION 5

Suppose that a jar contains 4 pens: 2 black, 1 blue, and 1 red.  Three people select a 
pen at random from the jar, sign a document, and replace the pen in the jar before the
next person selects a pen.  What is the probability that none of the people use the red
pen to sign the document?

A. 0.1406

B. 0.2500

C. 0.2813

D. 0.4219

E. 0.5000

QUESTION 6

A 30-question multiple choice test consists of 20 questions with four answer choices each
and 10 questions with five answer choices each.  What is the expected number of correct
answers that would result from random guessing?

A. 6

B. 7

C. 7.5

D. 8

E. None of These

QUESTION 7

Suppose that a pair of fair, standard 6-sided dice are rolled fifteen times.  What is
the probability that a sum of 7 occurs exactly three times in the fifteen rolls?

A. 0.0139

B. 0.0231

C. 0.2026

D. 0.2083

E. 0.2363

QUESTION 8

Suppose that 1,000 tickets are sold for a raffle.  If there is one prize of $2,500, two
prizes of $500, four prizes of $100, and thirteen prizes of $20, what is the expected
value of a raffle ticket?

A. $1.91

B. $4.16

C. $5.50

D. $6.76

E. None of These

QUESTION 9

Assuming that boys and girls are equally likely, what is the probability that a family
 with 6 children has exactly 3 boys and 3 girls?

A. 0.125

B. 0.1875

C. 0.25

D. 0.3125

E. 0.375

QUESTION 10

A restaurant manager estimates the likelihood that a newly hired waiter will still
 be working for the restaurant six months later is 60%.  If five new waiters are hired, 
what is the probability that at least four of them will still be working at the
restaurant six months later?

A. 0.1382

B. 0.2592

C. 0.3370

D. 0.4800

E. 0.7258