Question

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 repeat

the experiment above, what is the expected number of dice that have
an even roll?

Answer #1

We roll three fair six-sided dice.
(a) What is the probability that at least two of the dice land on a
number greater than 4?
(b) What is the probability that we roll a sum of at least
15?
(c) Now we roll three fair dice n times. How large need n be in
order to guarantee a better
than 50% chance of rolling a sum of at least 15, at least once?

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.

We roll two fair 6-sided dice, A and B. Each one of the 36
possible outcomes is assumed to be equally likely.
a. Find the probability that dice A is larger than dice B.
b. Given that the roll resulted in a sum of 5 or less, ﬁnd the
conditional probability that the two dice were equal.
c. Given that the two dice land on different numbers, ﬁnd the
conditional probability that the two dice differed by 2.

Suppose that we roll a pair of (6 sided) dice until the first
sum value appears that is 7 or less, and then we stop
afterwards.
a. What is the probability that exactly three
(pairs of) rolls are required?
b. What is the probability that at least three
(pairs of) rolls are needed?
c. What is the probability that, on the last
rolled pair, we get a result of exactly 7?

Two identical fair 6-sided dice are rolled
simultaneously. Each die that shows a number less than or equal to
4 is rolled once again. Let X be the number of dice that show a
number less than or equal to 4 on the first roll, and let Y be the
total number of dice that show a number greater than 4 at the
end.
(a) Find the joint PMF of X and Y . (Show your final
answer in a...

Imagine rolling two fair 6 sided dice. the number rolled on the
first die is even and the sum of the rolls is ten. are these two
events independent?

Imagine rolling two fair 6 sided dice. What is the probability
the number rolled on the first die is even or the sum of the rolls
is 10?

Consider rolling a fair 6-sided dice.
Which of the following statements are correct?
Group of answer choices
The probability that it lands on a 1 is 1/6.
The probability of an even number on one roll of a dice is
2/6.
The probability of an even number on one roll of a dice is
3/6.
If we roll this dice a large number of times, then for about 5/6
of the time, it will NOT land on a 2.
Suppose...

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) =

Consider the probability experiment consisting of rolling two
fair six-sided dice and adding up the result. (Recall: “fair” means
each side is equally likely.)
(a) Identify the sample space. S = { }
(b) Let W be the event that the dice roll resulted in the number
12.
Then P(W) =
(c) Classify the probability you found in the previous part
(circle one):
theoretical probability empirical probability subjective
probability
Explain your answer.
(d) Describe W0 in words (without using the...

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