Question

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?

Answer #1

If you roll a die, you get one of the following numbers: 1, 2,
3, 4, 5, 6. Each possibility occurs with equal probability of 1/6.
The expected value of a dice roll is E(D)= 3.5 and the variance of
a dice roll is Var(X) = 2.917.
a) Suppose you roll a die and then add 1 to the roll to get a
new random variable taking one of the following numbers:
2,3,4,5,6,7. What is the variance of this new...

How many ways are there to roll ten different 6-sided
die so that all six faces appear?

You roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 4 or an odd number

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).

You have a 4 sided die with sides marked A, B, C and
D. You roll the die 100 times. Find the
probablilty that you get A at least 92 % of the time.
Your friend also rolls the die from problem three 100 times. He
rolled more A’s than 70 % of all people who could roll this die 100
times. What percentage of the time did he roll and
A???

Consider an experiment where we roll 7 fair 6-sided dice
simultaneously (the results of the dice are
independent from each other).
(a) What is the probability that exactly 3 of the dice are greater
than or equal to 5?
(b) Suppose now that each of the 7 6-sided dice are weighted the
same such that the probability of
rolling a 6 is 0.5, and every other side that is not a 6 has equal
probability of being rolled. If we...

.
You roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 6 or an odd number
(a) P(6 or number greater than 3)=
(Round to three decimal places as needed.)

You roll a fair 6-sided die once and observe the result which is
shown by the random variable X. At this point, you can stop and win
X dollars. Or, you can also choose to discard the X dollars you win
in the first roll, and roll the die for a second time to observe
the value Y. In this case, you will win Y dollars. Let W be the
number of dollars that you win in this game.
a)...

For the following questions, find the
probability using a standard 6-sided die or two 6-sided dice. Write
your answer as a fraction or with a colon in lowest terms.
Rolling a single die, what is the probability of rolling an
even number?
Rolling a single die, what is the probability of rolling a
5?
Rolling a single die, what is the probability of rolling a
7?
Rolling a single die, what is the probability of rolling a
number less than...

You roll a six-sided die repeatedly until you roll a one. Let X
be the random number of times you roll the dice. Find the following
expectation:
E[(1/2)^X]

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