Question 1: Roll two fair dice. Then the sample space S is the
following.
S =...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...
I
am going to roll two dice one time and look at the sum.
Let event...
I
am going to roll two dice one time and look at the sum.
Let event A= sum is 8
Event B= sum is even
Event C= die 1 is a 3
1.Are events A and B Independent, dependent or mutually
exclusive? Why or why not?
2. Are events A and C independent, dependent or mutuallly
exclusive? Why or why not?
3. Are events B and C independent, dependent, or mutually
exclusive? Why or why not?
1. A random experiment consists of throwing a pair of dice, say
a red die and...
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...
You roll two six-sided fair dice. a. Let A be the event that the
first die...
You roll two six-sided fair dice. a. Let A be the event that the
first die is even and the second is a 2, 3, 4 or 5. P(A) = Round
your answer to four decimal places. b. Let B be the event that the
sum of the two dice is a 7. P(B) = Round your answer to four
decimal places. c. Are A and B mutually exclusive events? No, they
are not Mutually Exclusive Yes, they are Mutually...
In an experiment, two fair dice are thrown. (a) If we denote an
outcome as the...
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...
Suppose we roll 2 dice. One die is red, and the other is green.
Let event...
Suppose we roll 2 dice. One die is red, and the other is green.
Let event A = the sum is at most 5, and event B = the green die
shows a 3.
a) Find P(A) b) Find P(B) c) Find P(A and B) d) Find P(AIB) e)
Find P (BIA) f) Find P(A or B) g) Are events A and B
independent?
Consider the experiment of rolling two standard (six-sided) dice
and taking their sum. Assume that each...
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)...