Question

**Question I: You roll 2 fair dice, one red and one
green.**

**a) What is the probability that the red die does land on
4? does not land on 4?**

**b) What is the probability that either die lands on 4?
that neither die lands on 4?**

**c) What is the probability that the sum of the dice is
2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12?**

Answer #1

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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...

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 throw two fair dice, one green and one red, and observe the
numbers that came up.Take event A: the sum is 7, and event B: the
red die comes up even. Are these two events independent?

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.

Hector will roll two fair, six-sided dice at the same time. Let
A = the event that at least one die lands with the number 3 facing
up. Let B = the event that the sum of the two dice is less than
5.
1. What is the correct set notation for the event that “at least
one die lands with 3 facing up and the sum of the two dice is less
than 5”? 2. Calculate the probability that...

Suppose we roll 2 dice. One die is red, and the other is green.
Let event A = the sum is at most 5, and event B = the green die
shows a 3.
a) Find P(A) b) Find P(B) c) Find P(A and B) d) Find P(AIB) e)
Find P (BIA) f) Find P(A or B) g) Are events A and B
independent?

4 fair 10-sided dice are rolled.
(a)
Find the conditional probability that at least one die lands on
3 given that all 4 dice land on different numbers.
(b)
True or False: If X is the sum of the 4 numbers from
one roll, and Y is the maximum of the 4 numbers from one
roll, then X and Y are independent random
variables.

Let’s assume that there are two dice, and we will roll one of
them, but we don’t know which one. The probability of rolling
either dice is 1/2. One of them is fair in the sense that all 6
outcomes are equally likely. The other die gives probability 1/3 to
numbers 1 through 3 and zero probability to numbers 4-6.
a-)The first roll was a 4. What is the probability that it was
the fair die?
b-)The first roll was...

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

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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