Question

Two six-sided dice are rolled (one red and one green). Some
possibilities are (Red=1,Green=5) or (Red=2,Green=2) etc.

(a) How many total possibilities are there?

For the rest of the questions, we will assume that the dice
are fair and that all of the possibilities in (a) are equally
likely.

(b) What is the probability that the sum on the two dice comes
out to be 8?

(c) What is the probability that the sum on the two dice comes
out to be 12?

(d) What is the probability that the numbers on the two dice
are equal?

Answer #1

1. If two dice, one red and one green, are rolled, find the
probability that the red die shows a 3 and the green shows a
six.
2. If two dice are rolled, find the probability that the sum of
the faces of the dice is 7.

If a pair of dice, one green and one red, is rolled, what is the
probability that the following will occur? (Assume both dice are
six-sided. Enter your probabilities as fractions.)
(a) Pr(3 ≤ S ≤ 4), where S is the sum rolled
(b) Pr(8 ≤ S ≤ 11), where S is the sum rolled

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?

Probability. A six-sided fair dice has three green and three red
phases. Use a probability model to calculate the probability of the
sequences below. Based on the calculated probabilities which is the
sequence that is most likely to happen? (The correct answer with no
explanation/calculations will not get any points)
A) GRG
B) RR
C) RGRG
Probability. A fair six-sided die has two green and four red
faces and is balanced so that each face is equally likely to come...

involving the green and red 10-sided dice.
What is the probability that both dice show an even number?
What is the probability that the product of the numbers rolled
is less than 11?

17. Two dice (one red and one green)
are rolled, and the numbers that face up are observed. Test the
pair of events for independence.
A: The red die is 2, 4, or 5; B: The green die
is even.

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.

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.

A fair six-sided die has two sides painted red, 3 sides painted
blue and one side painted yellow.
The die is rolled and the color of the
top side is recorded.
List all possible outcomes of this random experiment
Are the outcomes equally likely? Explain
Make a probability distribution table for the random variable
X: color of the top side
2. If a pair of dice painted the same way as in problem 1 is
rolled, find the probability...

Suppose you roll two six-sided dice at once, one yellow and the
other green.
Find the probability that: (1) The yellow die shows 3 and the
green shows
5. (2) The yellow die is even and the green shows 1. (3) The sum
of the
two numbers shown is 6.

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