Question

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) =

Answer #1

Consider the following experiment of rolling two standard,
six-sided dice. Use the full sample space for rolling two standard,
six-sided dice. Use the sample space to calculate the
following.
Let E be the event that both face-up numbers are odd. Find
P(E).
Let F be the event that the face-up numbers sum to 7. Find
P(F).
Let T be the event that the sum of the face-up numbers is less
than 10. Find P(T).

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.

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).

Two standard six-sided dice are rolled. Report all answers in
reduced form (or rounded to two decimal places if applicable). What
are the odds for rolling a sum of 7? What is the probability of
rolling a product that is odd? What are the odds against rolling a
sum less than 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.)

A standard pair of six-sided dice is rolled. What is the
probability of rolling a sum less than or equal to 7? Express your
answer as a fraction or a decimal number rounded to four decimal
places.

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?

You roll two six-sided fair dice.
a. Let A be the event that either a 3 or 4 is rolled first
followed by an odd number.
P(A) = Round your answer to four decimal places.
b. Let B be the event that the sum of the two dice is at most
7.
P(B) = Round your answer to four decimal places.
c. Are A and B mutually exclusive events?
No, they are not Mutually Exclusive
Yes, they are Mutually Exclusive
d....

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?

Two fair six-sided dice are rolled once. Let (X, Y) denote the
pair of outcomes of the two rolls.
a) Find the probability that the two rolls result in the same
outcomes.
b) Find the probability that the face of at least one of the
dice is 4.
c) Find the probability that the sum of the dice is greater than
6.
d) Given that X less than or equal to 4 find the probability
that Y > X.

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