Question
In: Math
Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die...
Consider four nonstandard dice, whose sides are labeled as follows (the 6 sides on each die are equally likely).
A: 4, 4, 4, 4, 0, 0
B: 3, 3, 3, 3, 3, 3
C: 6, 6, 2, 2, 2, 2
D: 5, 5, 5, 1, 1, 1
These four dice are each rolled once. Let A be the result for die A, B be the result for die B, etc.
(a) Find P(A > B), P(B > C), P(C >D), and P(D > A).
(b) Is the event A > B independent of the event B > C? Is the event B > C independent of the event C >D? Explain.
Solutions
milcah answered 1 year agoRelated Solutions
Take a simple experiment of rolling a pair of balanced dice. Each die has six sides,...
Take a simple experiment of rolling a pair of balanced dice.
Each die has six sides, each side contains one to six spots. Let us
define the random variable x to be the sum of the spots on the two
dice. Display the probability mass function and the distribution
function for the random variable x.
You have two fair six-sided dice. The sides of each die are numbered from 1 to...
You have two fair six-sided dice. The sides of each die are
numbered from 1 to 6. Suppose you roll each die once. Let ? be
???(??? 1,??? 2), and let ? be ???(??? 1,??? 2).
a) Find the joint PMF of ? and ?.
b) Find ???(?).
c) Find ?[?+?]
Consider rolling two four sided dice. One die is blue and the other is green. (a)...
Consider rolling two four sided dice. One die is blue and the
other is green.
(a) State the sample space.
(b) Compute the probability of getting two even numbers.
(c) Compute the probability of getting an even sum if the blue
die rolls a 2.
What is the probability of drawing a four or a heart when
drawing a single card from a standard deck of cards.
Two 6-sided dice are rolled. One die is a standard die, and the other is a...
Two 6-sided dice are rolled. One die is a standard die, and the
other is a Fibonacci die with sides 1, 1, 2, 3, 5, and 8.
a. What is the probability distribution of this experiment?
b. What is the shape of the probability distribution?
c. What is the expected value when these 2 dice are rolled?
Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the...
Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are
tossed independently.
Let X = the minimum of the value from each die.
a. What is the probability mass function(pmf) of X?
b. Find the mean E[X] and variance V (X).
c. Write the cumulative distribution function (cdf) of X in a
tabular form.
d. Write F(x) the cdf of X as a step function and give a rough
sketch for this function.
a dice can have 6 sides and are numbered 1,2,3,4,5, and 6. The odds of getting...
a dice can have 6 sides and are numbered 1,2,3,4,5,
and 6. The odds of getting an odd number are the same. The chance
of getting an even number is the same. The chance of getting an odd
number is twice the chance of getting an even number.
a. Determine the opportunity to get the number 3.
b. The dice is thrown three times. Determine the odds of getting
two numbers 5 and one number 4.
c. The dice is...
Four standard dice were rolled. Then each die that did not come up six (any if)...
Four standard dice were rolled. Then each die that did not come
up six (any if) was rolled again. Following this, exactly one of
the four dice showed six on its upper face. Find the probability
that at least one of the four dice came up six on its initial
roll.
Consider a six-sided fair dice. Complete the following tables for this die: Number on the dice...
Consider a six-sided fair dice. Complete the following tables
for this die:
Number on the dice
Number of times it appears on the dice
Relative frequency of seeing that number
1
2
3
4
5
6
Total
This is the entire question, does not say how many times the
dice is thrown
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on
the sides (represented by painted spots). Imagine that such a die
is rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment. Compute the probability of
each of the following events. Event A: The sum is greater than 9.
Event B: The sum is not...
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides...
An ordinary (fair) die is a cube with the numbers 1 through 6 on
the sides (represented by painted spots). Imagine that such a die
is rolled twice in succession and that the face values of the two
rolls are added together. This sum is recorded as the outcome of a
single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9
Event B: The sum is not...
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