Question

Rolling Snake Eyes

- We roll two six-sided dice
*d*1 and*d*2. What is the probability that we roll two ones. (i.e., the probability that*d*1=*d*2=1). - We roll two six-sided dice
*d*1 and*d*2 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
*d*1 and*d*2 and at least one of the dice comes up as a one. What is the (conditional) probability that one of our dice came up 6. - We roll four six-sided dices
*d*1,…,*d*4 and at least one of these two events happened:

X)*d*1=1 and*d*3=1; or

Y)*d*2=1 and*d*4=1.

What is the (conditional) probability that*d*1=1 and*d*2=1? (Hint: Review the lecture on Anil's two children (Oct 31st))

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.

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?

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?

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?

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 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?

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).

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.

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...

what is the probability of rolling two standard six-sided dice
and getting the sum of least 8

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