Question

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.

Answer #1

(a)

The sample space for this experiment is as shown below:

S = { (1,1), (2,1), (3,1), (4,1), (5,1), (6,1), (1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (1,3), (2,3), (3,3), (4,3), (5,3), (6,3), (1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6), (6,6) }

There are total: 6*6 = 36 outcomes

(b)

The set that corresponds to the event that the number appearing on the first die is greater than that on the second is as shown below:

{(2,1), (3,1), (4,1), (5,1), (6,1),(3,2), (4,2), (5,2), (6,2),(4,3), (5,3), (6,3),(5,4), (6,4),(6,5) }

There are total 15 outcomes.

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)...

A pair of dice is rolled, and the number that appears uppermost
on each die is observed. Refer to this experiment, and find the
probability of the given event. (Enter your answer as a
fraction.)
The sum of the numbers is at least 4.
A pair of dice is rolled, and the number that appears uppermost
on each die is observed. Refer to this experiment and find the
probability of the given event. (Enter your answer as a
fraction.)
One...

1. a pair of fair dice is rolled. if the sum of the spots is 7,
determine the probability that one die showed a 2
2.what is the probability of rolling a sum of seven with a pair
of fair dice if one of them shows a five

Considering the 36 possible pairs of numbers (faces) when a pair
of fair dice is rolled.
1. Define two events that are mutually exclusive (also called
“disjoin events”). Apply your definition to the sample space of the
dice-rolling experiment and clearly state what the two typical
mutually exclusive events are.
2. Define two events that are statistically independent. Apply
your definition to the sample space of the dice-rolling experiment
and clearly state what the two typical statistically independent
events are.

In Exercises 7−14, a pair of fair dice is rolled.
7. What is the size of the sample space?
8. What is the probability of getting “snake eyes” (two 1s)?
9. What is the probability of getting doubles (the same number
on each die)?
10. What is the probability of getting a 1 on at least one
die?
11. What is the probability of getting a total of 7 on the two
dice?
12. What is the probability of getting...

Consider an experiment where a fair die is rolled repeatedly
until the first time a 3 is observed.
i) What is the sample space for this experiment? What is the
probability that the die turns up a 3 after i rolls?
ii) What is the expected number of times we roll the die?
iii) Let E be the event that the first time a 3 turns up is after
an even number of rolls. What set of outcomes belong to...

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.

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...

A pair of balanced dice is rolled once and the numbers on the
top of the dice are observed
Probability that the sum of the numbers on the tops of the dice
is 6 is ?
Probability that the 2nd number in the pair is larger than the
1st number is ?
Probability that the number on the top of the second die is 4 is
?
Probability that the numbers on the top of the dice are
different is...

A pair of balanced dice is rolled once and the numbers on the
top of the dice are observed.
Probability that the sum of the numbers on the tops of the dice
is 6 is?
Probability that the 2nd number in the pair is larger than the
1st number is?
Probability that the number on the top of the second die is 4
is?
Probability that the numbers on the top of the dice are
different is?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 34 minutes ago

asked 40 minutes ago

asked 42 minutes ago

asked 43 minutes ago

asked 44 minutes ago

asked 57 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago