Question

If you roll 1000 6-sided dice, what percentage of the time will the sum of all 1000 dice be a multiple of 4? (Order matters so for example, there are 1000 ways to have a sum of 1001).

Answer #1

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Suppose you roll two dice (normal six sided dice). What is the
probability that the sum of the spots on the up-faces is 4?

Suppose you roll two dice (normal six sided dice). What is the
probability that the sum of the spots on the up-faces is 4 or
8?

If you roll a 4-sided die and a 6-sided die at the same time and
then add the result on each of the dice, how many different ways
can you get a number greater than 7?

Suppose you roll a pair of six-sided dice.
What is the probability that the sum of the numbers on your dice is
at least 9?

You roll two fair six-sided dice. What is the probability that
the sum of the two dice values is exactly five? Be sure to count
all possible outcomes. (Hint: The event space has 36 distinct
outcomes).

Find the conditional probability, in a single roll of two fair
6-sided dice, that the sum is less than 6, given that the sum is
odd.

Two six-sided dice are rolled and the sum of the roll is
taken.
a) Use a table to show the sample space.
b) Find the Probability and the Odds of each event. E: the sum
of the roll is even and greater then 6
P(E) = O(E) =
F: the sum of the roll is 7 or less that 4
P(F) = O(F) =

2A.
What is the sample space of the following? Roll 2 four sided dice
and record the sum.
2B. If you roll a six sided die and a 4 sided die, what is the
probability that the sum will be 5?

Consider rolling two fair six-sided dice.
a) Given that the roll resulted in sum of 8, find the
conditional probability that first die roll is 6.
b) Given that the roll resulted in sum of 4 or less, find the
conditional probability that doubles are rolled.
c) Given that the two dice land on different numbers, find the
conditional probability that at least one die is a 6.

Suppose that you roll 117 fair six-sided dice. Find the
probability that the sum of the dice is less than 400. (Round your
answers to four decimal places.)

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