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Probability Theory and Binomial Probability Distribution - Prof. David W. Carter, Quizzes of Probability and Statistics

Various quizzes related to probability theory, including finding probabilities of events in experiments with marbles, dice, and coins. It also covers the binomial probability distribution, its mean, variance, and standard deviation. The exercises involve calculating probabilities, means, and standard deviations for specific experiments.

Typology: Quizzes

Pre 2010

Uploaded on 08/16/2009

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MATH 1530 – Quiz # 7 (Quizpak 3) Name _________________________
For exercises 1 and 2 consider a bag containing the following:
5 blue marbles numbered 1, 2, 3, 4, 5;
4 red marbles numbered 1, 2, 3, 4; and
3 green marbles numbered 1, 2, 3.
1. If ONE marble is to be randomly selected, find each of the following
probabilities.
GIVEN
P ( RED | 4 ) = _________________
P ( 4 | RED ) = _________________
2. If TWO marbles are randomly selected without replacement, find each of
the following probabilities.
P ( BLUE and GREEN ) = ____________________ = ___________
P ( BLUE and BLUE ) = ____________________ = ___________
pf3
pf4
pf5

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MATH 1530 – Quiz # 7 (Quizpak 3) Name _________________________

For exercises 1 and 2 consider a bag containing the following:

5 blue marbles numbered 1, 2, 3, 4, 5;

4 red marbles numbered 1, 2, 3, 4; and

3 green marbles numbered 1, 2, 3.

1. If ONE marble is to be randomly selected, find each of the following

probabilities.

GIVEN

P ( RED | 4 ) = _________________

P ( 4 | RED ) = _________________

2. If TWO marbles are randomly selected without replacement, find each of

the following probabilities.

P ( BLUE and GREEN ) = ____________________ = ___________

P ( BLUE and BLUE ) = ____________________ = ___________

MATH 1530 – Quiz # 8 (Quizpak 4) Name _________________________

Consider the experiment of rolling two “fair” 4-sided die and recording the

number facing down (either 1, 2, 3, or 4) on each of the two die.

Let X be the random variable such that:

Complete the table that gives the probability distribution for this particular

experiment.

X P(X)

X = the sum of the two die

Consider a binomial experiment S S

With two independent trials, where S F

the probability of success is given by: F S

p = .4 F F

Complete the table that gives the probability

distribution for this particular experiment to the right.

Show the binomial formulas here:

P ( X = 0 ) = ___________________________________ = _____________

P ( X = 1 ) = ___________________________________ = _____________

P ( X = 2 ) = ___________________________________ = _____________

(Specific Formula) (Numerical Value)

Show the formulas and calculate each of the following:

The mean

= ____________ = ______________ = _________

The variance

2

 = ____________ = ______________ = _________

The standard deviation^ ^ = ____________ = ______________ = _________

(General Form.) (Specific Form.) (N. V.)

MATH 1530 – STATDISK WORKSHEET – CHAPTER 3 Name ______________________________

Let X = the # of successes

in two trials

X P(X)

*For all random generators use SEED = 3.

3.1 Enter the estimated probability here, as a fraction then decimal.

P x ( 3) = __________ = __________

*For exercises 3-2 through 3-8, use n = 1000.

3-2 Enter the probability for getting a sum of 7 here. __________ = __________

3-3 Enter the probability for getting a sum of 10 here. __________ = __________

3-5 Enter the probability for getting exactly 11 heads here. __________ = __________

3-7 Enter the probability for getting AT LEAST 55 girls out of 100__________ = __________

3-9 What is the estimated probability of winning if you bet on a single number like “7” every

time?

P x ( 7) (^) = __________ = __________

3-14 Enter the estimated probability here. __________ = __________

3-16 a. Find P (90  x 110) = __________ = __________

b. Find P x (  115) = __________ = __________

c. Find P x (^^ ^ 120) = __________ = __________

3-17 a. P x (^^ 1)^ = ______ = __________

5

b. P x (^^ 1)^ = ______ = __________

25

c. P x (^^ 1)^ = ______ = __________

50

d. P x (^^ 1)^ = ______ = __________

500 How far off from.

did we end up?

e. P x ( 1) = ______ = __________

1000 _____________________

MATH 1530 – STATDISK WORKSHEET – CHAPTER 4 Name _______________________

The following notes will be provided for your reference as the last page of Exam 2:

Chapter 3 – Probability

Rule of Complementary Events:

Formal Addition Rule (OR):

P(A or B) = P(A) + P(B) – P(A and B)

Multiplication Rule (AND):

P (King 2nd | King 1st) =

(Three Kings are left out of only 51 cards.)

P (King 1st AND King 2nd) =

  (King on 2

nd has different probability given King 1

st .)

NOT Independent P (A and B) = P (A) ^ P (B|A) (Formal Rule)

P (Head and Head) =

  (Independent – first toss does not affect probability for 2

nd .)

Independent P (A and B) = P (A) ^ P (B)

Chapter 4 – Probability Distributions

For ANY Probability Dist.: 1.  P x ( )^^ ^1

2. The Mean, ^ ^  x^  p x ( )

3. The Variance,

2 2 2    xp x ( )

4. The Standard Dev.

2 2   xp x ( )

The BINOMIAL Probability Distribution:

The Mean,

  np

The Variance,

2   n   p q

The Standard Deviation, ^ ^ n^   p q

P(A) + P( A ) = 1

P( A ) = 1 – P(A)

P (A) = 1 – P( A )

The Binomial

Probability Formula

x n x

n x

P x C p q