Question

Suppose you plan to roll a fair six-sided die two times. What is the probability of rolling a ‘1’ both times?

Group of answer choices

Answer #1

5. Suppose the six-sided die you are using for this
problem is not fair. It is biased so that rolling a 6
is three times more likely than any other roll. For this
problem, the experiment is rolling a six-sided die twice.
(A): What is the probability that one or both rolls are even
numbers (2, 4 or 6’s)?
(B): What is the probability that at least one of the rolls is
an even number or that the sum of...

Assume that a fair
six-sided die is rolled 9 times, and the roll is called a success
if the result is in {1,2}{1,2}.
What is the probability that there are exactly 4 successes or
exactly 4 failures in the 9 rolls?

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?

You flip a fair coin. If the coin lands heads, you roll a fair
six-sided die 100 times. If the coin lands tails, you roll the die
101 times. Let X be 1 if the coin lands heads and 0 if the coin
lands tails. Let Y be the total number of times that you roll a 6.
Find P (X=1|Y =15) /P (X=0|Y =15) .

Suppose we roll a fair six-sided die and sum the values obtained
on each roll, stopping once our sum exceeds 376. Approximate the
probability that at least 100 rolls are needed to get this sum.
Probability =

1. Suppose you have a fair 6-sided die with the numbers 1
through 6 on the sides and a fair 5-sided die with the numbers 1
through 5 on the sides. What is the probability that a roll of the
six-sided die will produce a value larger than the roll of the
five-sided die?
2. What is the expected number of rolls until a fair five-sided
die rolls a 3? Justify your answer briefly.

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...

You roll a normal 6-sided die. What is the probability of
rolling at least one 5 if you roll 3 times?

You roll a six-sided
die.
What are the odds of
rolling a multiple of 2?

You roll a six-sided die. Find the probability of each of the
following scenarios.
(a) Rolling a 6 or a number greater than 3
(b) Rolling a number less than 5 or an even number
(c) Rolling a 4 or an odd number

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