Question

2A.
What is the sample space of the following? Roll 2 four sided dice
and record the sum.

2B. If you roll a six sided die and a 4 sided die, what is the
probability that the sum will be 5?

Answer #1

A) Here, we are rolling the 2 four sided dice then the all possible
outcome are as follows,

S={(1,1),(1,2),(1,3),(1,4),

(2,1,(2,2),(2,3),(2,4),

(3,1),(,3,2),(3,3),(3,4),

(4,1),(4,2),(4,3),(4,4)}

n(S)= 16

Let S1 be the sample space of sum of outcomes when the 2 four sided
dice is rolled .

Then the possible sum of each outcome are as follows,

S1={2,3,4,5,6,7,8}

n(S1)=7

B) let S be the sample space of a rolling of a six dice and a 4
sided dice then the all possible outcome is,

S={(1,1),(1,2),(1,3),(1,4),

(2,1,(2,2),(2,3),(2,4),

(3,1),(,3,2),(3,3),(3,4),

(4,1),(4,2),(4,3),(4,4),

(5,1),(5,2),(5,3),(5,4),

(6,1)(6,2),(6,3),(6,4)}

n(S)= 24

Let A be the event that sum of the outcome is 5,

A={(1,4),(2,3),(3,2),(4,1)}

n(A)=4

By definition of the probability,

P(A)= n(A)/n(S)

= 4/24

=1/6

The probability that the sum will be 5 is 1/6

What is the sample of the following?
A. Roll a six sided die and record the result
B. Roll 2 four sided die and record the sum

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 two dice (normal six sided dice). What is the
probability that the sum of the spots on the up-faces is 4?

1. Game of rolling dice
a. Roll a fair die once. What is the sample space? What is the
probability to get “six”? What is the probability to get “six” or
“five”?
b. Roll a fair die 10 times. What is the probability to get
“six” twice? What is the probability to get six at
least twice?
c. Roll a fair die 10 times. What is the expected value and
variance of getting “six”?
d. If you roll the die...

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 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) =

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
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outcomes).

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Suppose you roll six-sided dice four times and write down the
resulting four digit number. We sat that a number is "balanced" if
it contains an equal number of even and odd terms. What is the
probability that the result of rolling the die is balanced?

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