Question

You have a 4 sided die and 10 sided die that are rolled 50 times. What is the theoretical probability that the small die is odd, the sum of the numbers is 5, the same # appears on both, the # on the larger die is > than the # on the smaller die.

Answer #1

There are a total of 4*10 = 40 outcomes for the result on the two dice throws here.

a) The probability that the small die is odd is computed here
as:

= P(X = 1 or X = 3) = 2/4 = 0.5

**Therefore 0.5 is the required probability
here.**

b) P(sum of the numbers is 5) = P(14, 23, 32, 41) = 4/40 =
0.1

**Therefore 0.1 is the required probability
here.**

c) The probability that same number appears on both is computed
here as:

P( 11 or 22 or 33 or 44) = 4/40 = 0.1

**Therefore 0.1 is the required probability
here.**

d) The probability that number on larger die is greater than on
smaller die is computed here as:

= P(X = 1, Y > 1) + P(X = 2, Y > 2) + P(X = 3, Y = 3) + P(X =
4, Y > 4)

= (1/4)*(0.9 + 0.8 + 0.7 + 0.6)

= 0.25*(3) = 0.75

**Therefore 0.75 is the required probability
here.**

Q -
Die A is rolled 50 times and a 6 is scored 4 times,
while a 6 is obtained 10 times when die B is rolled
50 times.
A). Construct a two-sided 98% confidence interval
for the difference in the probabilities of scoring
a 6 on the two dice.
B). Calculate the test statistics for the two- sided
null
hypothesis that the two dice have equal
probabilities of scoring a 6.
C). Calculate a p-value for the two-sided null...

Die A is rolled 50 times and a 6 is scored 4 times, whilea 6 is
obtained 10 times when die B is rolled 50 times.
Calculate the test statistics for the two-sided null hypothesis
that the two dice have equal probabilities of scoring a 6.
-2
-1.5
-1.729
-1.63

A fair 4-sided die and a fair 6-sided die will be rolled. A)
Give the sample space. B) What is the probability the sum is 9? C)
What are the chances that the sum is 4, or the 4 sided die comes up
a 3?

Die A is rolled 50 times and a 6 is scored 4 times, whilea 6 is
obtained 10 times when die B is rolled 50 times.
Construct a two-sided 98% confidence interval for the difference
in the probabilities of scoring a 6 on the two dice.
(-0.2074, -0.0325)
(-0.2324, -0.0075)
(-0.2792, 0.0392)
(-0.2960, 0.0560)

A 10 sided die with sides numbered 0 through 9 is rolled 5
times. Let X be the number of zeros rolled.
(a) Find the probability that exactly 2 zeros are rolled.
(b) Find the probability that no less than 4 zeros are
rolled.
(c) Find the mean and the variance of X.

A six-sided die is rolled 10 times and the number of times the
six is rolled is recorded. This is an example of a binomial
experiment.
Select one:
True
False

1) A 10-sided die is rolled infinitely many times. Let X be the
number of rolls up to and including the first roll that comes up 2.
What is Var(X)?
Answer: 90.0
2) A 14-sided die is rolled infinitely many times. Let X be the
sum of the first 75 rolls. What is Var(X)?
Answer: 1218.75
3) A 17-sided die is rolled infinitely many times. Let X be the
average of the first 61 die rolls. What is Var(X)?
Answer:...

4 fair 10-sided dice are rolled.
(a)
Find the conditional probability that at least one die lands on
3 given that all 4 dice land on different numbers.
(b)
True or False: If X is the sum of the 4 numbers from
one roll, and Y is the maximum of the 4 numbers from one
roll, then X and Y are independent random
variables.

Run a simulation of two, 6-sided (fair) dies being rolled 5,000
each. The two die are rolled at the same time, and the sum is
recorded. Find the probability the sum is larger than 9. Solve in
SAS , give SAS formula/equation. SAS or EXCEL

A fair 4-sided die is rolled 7 times.
(a)
Find the probability that the side 1 comes up exactly 3
times.
(b)
Find the probability that there is at least one side that comes
up exactly 3 times.

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