Question

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 word “not”).

(e) Find P(W0) and explain how you found it.

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.

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 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).

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 4 or 9.

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 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...

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?

41. A probability experiment consists of rolling a
sixteen-sided die and spinning the spinner shown at the right. The
spinner is equally likely to land on each color. Use a tree diagram
to find the probability of the given event. Then tell whether the
event can be considered unusual.Event: rolling a A spinner 15 and
the spinner landing on yellow.
The probability of the event is:___
40.
A probability experiment consists of rolling a twelve-sided die
and spinning the spinner...

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...

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?

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