In: Statistics and Probability

An experiment is rolling two fair dice and adding the spots
together. Find the following probabilities; **enter all
answers as simplified fractions using the / bar between numerator
and denominator, with no extra space**

**Blank #1:** Find the probability of getting a sum
of 3.

**Blank #2:** Find the probability of getting the
first die as a 4.

**Blank #3:** Find the probability of getting a sum
of 8.

**Blank #4:** Find the probability of getting a sum
of 3 or sum of 8.

**Blank #5:** Find the probability of getting a sum
of 3 or the first die is a 4.

**Blank #6:** Find the probability of getting a sum
of 8 or the first die is a 4.

**Blank #7:** Find the probability of not getting a
sum of 8.

please make it clear to read and explain how to do it.

probabilities Find the probabilities for each
event. Consider rolling a pair of fair dice two times. Let
A be the total on the up-faces for the first roll and let
B be the total on the up-faces for the second roll.
A = {2 on the first roll}, B = {8 or more on
the first roll}.
A = {2 on the first roll}, B = {8 or more on
the second roll}.
A = {5 or less on the...

When you have two dice rolling at the same time, find the
following probabilities with proper explanations.
(1) When you will observe a total of 8
(2) When you will observe a total of 4 or a total of 6
(3) When you will observe at least a total of 2

When you have two dice rolling at the same time, find the
following probabilities with proper explanations.
(1) When you will observe a total of 8
(2) When you will observe a total of 4 or a total of 6
(3) When you will observe at least a total of 2

Consider the experiment of rolling two dice and the following
events:
A: 'The sum of the dice is 8'
and B: 'The first die is an odd number' and
C: "The difference (absolute value) of the dice is
2"
Find (a) p(A and B) (HINT: You cannot
assume these are independent events.)
(b) p(A or
B)
(c) Are
A and B mutually exclusive events? Explain.
(d) Are A and B independent events?
Explain.
(e) Are B and C independent events?
Explain.

Find the probability that:
Rolling a fair die 3 times, at least two dice are less than
4.
Previous answers have suggested 0.875 (189 feasible cases/ 216
total cases). However, from simple trial and error we can see that
there are more than 27 cases where this answers fails. For example
is the first dice gets a 4 and the 2nd dice gets 4,5,6 and the last
dice gets any number, there is already 18 cases here that are not...

I. Consider the random experiment of rolling a pair of dice.
Note: Write ALL probabilities as reduced fractions or whole numbers
(no decimals).
1) One possible outcome of this experiment is 5-2 (the first die
comes up 5 and the second die comes up 2). Write out the rest of
the sample space for this experiment below by completing the
pattern:
1-1
2-1
1-2
1-3
1-4
1-5
1-6
2) How many outcomes does the sample space contain?
_____________
3) Draw...

I. Consider the random experiment of rolling a pair of dice.
Note: Write ALL probabilities as reduced fractions or whole numbers
(no decimals).
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
2) How many outcomes does the sample space contain?
_____36________
3)Draw a circle (or shape) around each of the following events...

An experiment consists of rolling three fair dice --- a red die,
a blue die, and a white die --- and recording the number rolled on
each die. Assume that the dice are fair, so that all outcomes are
equally likely. (1) What probability should be assigned to each
outcome? equation editorEquation Editor (2) What is the probability
that the sum of the numbers rolled is 5? equation editorEquation
Editor (3) What is the probability that the sum of the...

7. [10
marks] Consider an experiment of rolling two regular (or
fair) balanced six-sided dice. a) List out all the possible
outcomes.
b) Define X as the amount you will win
in the following game.
You will win $100 when a double (two
identical numbers) is rolled; you will win $10 when an odd sum is
rolled; and you will win $30 when other even sum is rolled,
excluding doubles. Define X as the amount you will win in this...

for the experiment of rolling an ordinary pair of
dice, find the probability that the sum will be even or a multiple
of 6. ( you may want to use a table showing the sum for each of the
36 equally likely outcomes.)

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