In Yahtzee, a “large straight” is a roll that leads to five dice
displaying 1-2-3-4-5 or...
In Yahtzee, a “large straight” is a roll that leads to five dice
displaying 1-2-3-4-5 or 2-3-4-5-6. What is the probability that a
player will score a large straight with a single roll of all six
dice?
Question:
You have five dice, like in a game of Yahtzee! Suppose you roll
the five dice once and sum the numbers the five dice show.
(a) What is the mean and the standard deviation of the sum of
five dice?
(b) Suppose you average 60 of such rolls with the five dice.
What is the distribution of this average?
(c) What is the chance the average of 60 such rolls is larger
than 18?
1. A round in the game Yahtzee begins by rolling five fair dice.
Find the probability of rolling a:
a. one pair (ex 33421 but not 33441), two pair (ex 33441 but not
33444), and three of a kind (ex 24252 but not 24242)
2. Consider a 10x10 matrix that consists of all zeros. ten
elements of the matrix are selected at random and their value is
changed from a zero to a one. find the probability that the ones...
Each of 3 fair dice has six sides numbered 1, 2, 3, 4, 5, and 6.
If these 3 dice are all rolled at the same time, what is the
probability that exactly 2 of these dice will show a 1 ?
Answers in word version please
You roll a die 48 times with the following results.
Number
1
2
3
4
5
6
Frequency
3
1
15
13
4
12
Use a significance level of 0.05 to test the claim that the die is
fair.
(PLEASE SHOW ALL YOUR WORK)
We will simulate a dice game in which 2 dice are thrown.
If the roll is 7 or 11, you win.
If the roll is 2, 3, or 12, you lose
If the roll is any other value, it establishes a
point.
If with a point established, that point is rolled again before
a 7, you win.
If, with a point established, a 7 is rolled before the point is
rolled again you lose.
Build your algorithm incrementally. First write...
1) Imagine you roll a fair 4 sided dice 4 times.
what is the number of possible outcomes as a sum of successes?
2) What is the probability you will roll 3 successes,
if the result of a 4 is considered a success?
3) what is the probability you will roll 3 or 4 successes, of the
results of a 4 is considered a success?
4) what is the probability you will roll 3 or 4
successes. of the result...
4.
(a) Suppose that τσ=(1 5 2 3)(4) and στ=(1 2 4 5)(3) in S5. If
σ1 = 2, find σ and τ.
(b) In Sn, show that σ = τ if and only if σ(τ)^(−1) = ε. ε is
the identity permutation. Must be written as a proof.
(c) Let σ=(1 2 3) and τ=(1 2) in S3. Show that
S3={ε,σ,σ^2,τ,τσ,τ(σ)^2} and that σ^3=ε=τ^2 and στ=τ(σ)^2, then
fill out the multiplication table for S3.
coffee tea juice
3
4
5
5
4
3
4
4
4
5
1
2
4
2
2
Do a One-way ANOVA by hand (at least once in
your life!) …Is there a difference in attention for those who drink
coffee, tea, or juice during an 8 a.m. class? Utilize the five
steps of hypothesis testing to analyze the following data
(p<.01).
Attention Ratings (1=no attention-
5=full attention)
Find the distances:
A) Between ?1=〈2+2?,−1+?,−3?〉and ?2=〈4,−5−3?,1+4?〉 .
B) Between the planes 2?−?+5?=0 and 2?−?+5?=5 .
C) From the point (1,2,3) to the line ?=〈−?,4−?,1+4?〉 .