Question
In: Statistics and Probability
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9
Event B: The sum is not divisible by 6
Round your answers to two decimal places.
P(A) =
P(B) =
Solutions
orchestra answered 1 year agoRelated Solutions
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on
the sides (represented by painted spots). Imagine that such a die
is rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment. Compute the probability of
each of the following events. Event A: The sum is greater than 9.
Event B: The sum is not...
An ordinary (fair) die is a cube with the numbers through on the sides (represented by...
An ordinary (fair) die is a cube with the numbers through on the
sides (represented by painted spots). Imagine that such a die is
rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment. Compute the probability of
each of the following events.
Event A : The sum is greater than 5 .
Event B: The sum is an...
a. When a fair die is thrown, numbers 1 through 6 would appear with equal probability of...
a. When a fair die is thrown, numbers 1 through 6
would appear with equal probability of 1/6. The mean is 3.5 and
variance is 2.92.
If 57 dice are thrown, what is the variance of their sum?
b .
When a fair die is thrown, numbers 1 through 6 would appear with
equal probability of 1/6. The mean is 3.5 and variance is 2.92.
If 40 dice are thrown, what is the mean of their sum?
c.
Let X be...
Suppose you roll a fair 15 sided die. The numbers 1-15 appear once on different sides....
Suppose you roll a fair 15 sided die. The numbers 1-15 appear
once on different sides. (Imagine a regular die with 12 sides
instead of 6.) Answers may be left in formula form.
(a) What is the probability of rolling a 7?
(b) What is the probability of rolling an odd number and a
number greater than 8?
(c) What is the probability of rolling an even number or a
number greater than 9?
(d) Suppose you roll the die,...
Suppose we roll a fair 6 sided die with the numbers [1,6] written on them. After...
Suppose we roll a fair 6 sided die with the numbers [1,6]
written on them. After the first die roll we roll the die ? times
where ? is the number on the first die roll. The number of points
you score is the sum of the face-values on all die rolls (including
the first). What is the expected number of points you will
score?
Consider that you toss a fair 6-sided die containing the numbers 1-2-3-4-5-6 and also toss a...
Consider that you toss a fair 6-sided die containing the numbers
1-2-3-4-5-6 and also toss a fair 4-sided die containing the numbers
1-2-3-4. Find the probability distribution for the sum of the
values on the two dice. Also, find the mean and the variance of
this probability distribution.
Please provide a well written and well explained answer.
Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6...
Consider rolling both a fair four-sided die numbered 1-4 and a
fair six-sided die numbered 1-6 together. After rolling both dice,
let X denote the number appearing on the foursided die and Y the
number appearing on the six-sided die. Define W = X +Y . Assume X
and Y are independent.
(a) Find the moment generating function for W.
(b) Use the moment generating function technique to find the
expectation.
(c) Use the moment generating function technique to find...
Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X...
Consider a fair four-sided die numbered 1-4 and a fair six-sided
die numbered 1-6, where X is the number appearing on the
four-sided die and Y is the number appearing on the
six-sided die. Define W=X+Y when they are rolled
together. Assuming X and Y are
independent, (a) find the moment generating function for
W, (b) the expectation E(W), (c) and the variance
Var(W). Use the moment generating function technique to
find the expectation and variance.
You have two fair six-sided dice. The sides of each die are numbered from 1 to...
You have two fair six-sided dice. The sides of each die are
numbered from 1 to 6. Suppose you roll each die once. Let ? be
???(??? 1,??? 2), and let ? be ???(??? 1,??? 2).
a) Find the joint PMF of ? and ?.
b) Find ???(?).
c) Find ?[?+?]
Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die...
Consider four nonstandard dice, whose sides are labeled as
follows (the 6 sides on each die are equally likely).
A: 4, 4, 4, 4, 0, 0
B: 3, 3, 3, 3, 3, 3
C: 6, 6, 2, 2, 2, 2
D: 5, 5, 5, 1, 1, 1
These four dice are each rolled once. Let A be the result for
die A, B be the result for die B, etc.
(a) Find P(A > B), P(B > C), P(C >D),...
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