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 die is rolled twice. Let X be the maximum of the two
rolls. Find the distribution of X.
Let Y be the minimum of the two rolls. Find the variance of
Y.
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 one dice is rolled (die 1, die 2), find the probability of
getting sum less than 11?
a. What is the probability experiment? Rolling a dice (die 1,
die 2)
b. What is the event(s)? sum greater than 11
c. What technique can I use to solve this problem? Select an
answer
d. How do you know you can use that technique? Select an
answer
f. Find the probability of rolling a sum that is sum less than
11....
A regular six-sided die and a regular eight-sided die are rolled
to find the sum. Determine the probability distribution for the sum
of the two dice. Create a frequency histogram for the probability
distribution and determine the expected sum of the two dice.
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...