Question

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)

e. Find A u B and P(A u B)

Q2) Two fair dice are rolled.

a. What's the most likely sum? Why?

b. What are the least likely sums? Why?

Answer #1

In an experiment, two fair dice are thrown. (a) If we denote an
outcome as the ordered pair (number of dots on the first die,
number of dots on the second die), write down the sample space for
the experiment. (So a roll of “1 dot” on the first die and a roll
of “3 dots” on the second die would be the ordered pair (1, 3) in
the sample space S.) You can think of the first die as...

please answer the following questions:
*An experiment consists of rolling two dice. Find the
probability that the sum is greater than or equal to 9 or
even.
*A die is rolled. find
a- sample space for the experiment.
b- event of rolling an even number.
c- probability of rolling at least a number 3.

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)...

A pair of fair dice is rolled.
(a) What is the sample space of this experiment?
(b) Describe the set that corresponds to the event that the
first die lands on a strictly higher value than the second die.

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 9.

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 4 or 9.

Give the probability of rolling a pair of fair dice such
that:
a. both dice come up odd.
b. at least one die comes up odd.
c. exactly one die comes up odd.
d. the sum of the dice is odd.

Two fair dice are rolled.
(a) Find the conditional probability doubles are rolled, given
the sum is eight.
(b) Find the conditional probability the sum is eight, given
doubles are rolled.
(c) Find the probability at least one die lands on six.
(d) Find the conditional probability at least one die lands on
six, given that doubles are not rolled.

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.

Hector will roll two fair, six-sided dice at the same time. Let
A = the event that at least one die lands with the number 3 facing
up. Let B = the event that the sum of the two dice is less than
5.
1. What is the correct set notation for the event that “at least
one die lands with 3 facing up and the sum of the two dice is less
than 5”? 2. Calculate the probability that...

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