Question

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?

Answer #1

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.

Rolling Snake Eyes
We roll two six-sided dice d1 and d2. What is
the probability that we roll two ones. (i.e., the probability that
d1=d2=1).
We roll two six-sided dice d1 and d2 and at
least one of the dice comes up as a one. What is the (conditional)
probability that we roll two ones.
We roll two six-sided dice d1 and d2 and at
least one of the dice comes up as a one. What is the (conditional)
probability...

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).

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...

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.)

Four fair six sided dice are rolled. Given that at least two of
the dice land on an odd number, what is the probability that the
sum of the result of all four dice is equal to 14?

If you roll four (six-sided) dice, what is the probability that
at least one dice will be different from the other three? Leave
answer as a fraction

Suppose we roll a fair six-sided die and sum the values obtained
on each roll, stopping once our sum exceeds 376. Approximate the
probability that at least 100 rolls are needed to get this sum.
Probability =

roll a pair of fair dice and at least one of the dice is a
six.
without any further information to go on, what is the
conditional probability that the sum of the dice is 8? Is the event
that “sum is 8” independent from the event that “at least one of
the dice is a six”?

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?

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