Question

Consider the experiment of rolling two standard (six-sided) dice and taking their sum. Assume that each die lands on each of its faces equally often. We consider the outcomes of this experiment to be the ordered pairs of numbers on the dice, and the events of interest to be the different sums.

Write out the generating function F(x) for the sums of the dice, and show how it factors into the generating functions for the individual die rolls.

Use F(x) to find another pair of dice, not identical to each other, that give the same probabilities of their sum as normal dice. (Hint: how else can you factor F(x)?)

Answer #1

**Solution**

**Given that**

A experiment consists of rolling two 6-sided dice and observing
the sum of the upper faces.
1.) determine the random variable, X.
2.) What values can X take on?
3.) how many possible outcomes are there for this experiment
?
D.) Create a probability distribution for X.

Question:
Q1) An experiment consists of rolling two fair dice and
recording the outcome as an ordered pair: (#1st die, #2nd die).
a. Find the sample space S of the experiment (list each
outcome).
b. Let A be the event that the sum of the dice is 4. Find A and
P(A)
c.Let B be the event that at least one of the dice lands on 3.
Find B and P(B).
d. Find A n B and P(A n B)...

Consider the following experiment of rolling two standard,
six-sided dice. Use the full sample space for rolling two standard,
six-sided dice. Use the sample space to calculate the
following.
Let E be the event that both face-up numbers are odd. Find
P(E).
Let F be the event that the face-up numbers sum to 7. Find
P(F).
Let T be the event that the sum of the face-up numbers is less
than 10. Find P(T).

1. A random experiment consists of throwing a pair of dice, say
a red die and a green die, simultaneously. They are standard
6-sided dice with one to six dots on different faces. Describe the
sample space.
2. For the same experiment, let E be the event that the sum of
the numbers of spots on the two dice is an odd number. Write E as a
subset of the sample space, i.e., list the outcomes in E.
3. List...

1) An experiment consists
of throwing two six-sided dice and observing the number of spots on
the upper faces. Determine the probability that
a.
the sum of the spots is 3.
b.
each die shows four or more spots.
c.
the sum of the spots is not 3.
d.
neither a one nor a six appear on each die.
e.
a pair of sixes appear.
f.
the sum of the spots is 7.

Consider rolling two fair six-sided dice.
a) Given that the roll resulted in sum of 8, find the
conditional probability that first die roll is 6.
b) Given that the roll resulted in sum of 4 or less, find the
conditional probability that doubles are rolled.
c) Given that the two dice land on different numbers, find the
conditional probability that at least one die is a 6.

Imagine rolling two fair 6 sided dice. the number rolled on the
first die is even and the sum of the rolls is ten. are these two
events independent?

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum greater than 3 ? Express your answer
as a decimal number rounded to three decimal places.

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than 3? Express your answer as a
fraction or a decimal number rounded to four decimal places.

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than 10? Express your answer as a
fraction or a decimal number rounded to four decimal places.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 38 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago