In: Statistics and Probability

a fair 6-sided die is rolled three times. What is the probability that all three rolls are 2? Round the answer to four decimal places

A fair 6-sided die is rolled repeatedly. (a) Find the expected
number of rolls needed to get a 1 followed right away by a 2. Hint:
Start by conditioning on whether or not the first roll is a 1. (b)
Find the expected number of rolls needed to get two consecutive
1’s. (c) Let an be the expected number of rolls needed to get the
same value n times in a row (i.e., to obtain a streak of n
consecutive...

Suppose a 6-sided die and a 7-sided die are rolled. What is the
probability of getting sum less than or equal to 5 for the first
time on the 4th roll? Show your work to receive credit.

A fair red die and a fair green die are rolled.
(a) What is the probability that the sum of the numbers is
even?
(b) What is the probability that the number on the red die is
more than the number on the green die?
(c) What is the probability that the number on the red die is
twice the number on the green die?
(d) What is the probability that the number on the red die is
different from...

Problem 28. A fair six-sided die is rolled repeatedly and the
rolls are recorded. When two consecutive rolls are identical, the
process is ended. Let S denote the sum of all the rolls made. Is S
more likely to be even, odd or just as likely even as odd?

A fair six-sided die is rolled repeatedly until the third time a
6 is rolled. Let X denote the number of rolls required until the
third 6 is rolled. Find the probability that fewer than 5 rolls
will be required to roll a 6 three times.

If a fair coin is flipped twice and a standard 6 sided die is
rolled once, what is the likelihood of getting two 'heads' on the
coin and a '1' on the die? â€‹Express your answer as a percent
rounded to the tenth place

Example 4: A fair six-sided die is rolled six times. If
the face numbered k is the outcome on roll k for k = 1, 2, 3, 4, 5,
6 we say that a match has occurred. The experiment is called a
success if at least one match occurs during the six trials.
Otherwise, the experiment is called a failure. The outcome space is
O = {success, failure}. Let event A = {success}. Which value has
P(A)?
**This question has...

A fair six-sided green die is rolled resulting in a number
between 1 and 6. Then that number of red dice are rolled. Find the
expected value and variance of the sum of the red dice.

When a fair die is rolled n times, the probability of getting at
most two sixes is 0.532 correct to three significant figures. (a)
Find the value of n. ( Can help without using a GDC or write down
steps on how to find answer from GDC. not just stating .. I know
the answer is 15 but l need working steps on how to get 15
clear?)

You roll a fair die three times. What is the probability of each
of the following?
a) You roll all 4's.
b) You roll all even numbers.
c) None of your rolls gets a number divisible by 3.
d) You roll at least one 2.
e) The numbers you roll are not all 2's.

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