Question

**Using Python :**

consider the following experiment:

You roll a pair of fair dice and calculate the sum of the faces.

You are interested in the number of rolls it takes until you get a sum of "7". The first time you get a "7" the experiment is considered a "success". You record the number of rolls and you stop the experiment. You repeat the experiment N=100,000 times. Each time you keep track of the number of rolls it takes to have "success".

After the N experiments are completed you should generate a probability mass function for the number of rolls it takes for "success".

Answer #1

You roll a pair of fair dice 20 times. Each time, the sum of the
two dice values is recorded. What is the probability that you will
roll an 7 (the sum of the two dice values = 7) at least (5) times?
Assuming that each roll of the dice is independent

You roll a pair of fair dice repeatedly. Let X denote the number
of rolls until you get two consecutive sums of 8(roll two 8 in a
row). Find E[X]

Suppose that we roll a pair of (6 sided) dice until the first
sum value appears that is 7 or less, and then we stop
afterwards.
a. What is the probability that exactly three
(pairs of) rolls are required?
b. What is the probability that at least three
(pairs of) rolls are needed?
c. What is the probability that, on the last
rolled pair, we get a result of exactly 7?

Problem:
Roll a pair of fair dice. Find the probability that:
a) On an individual roll, the sum is 5 or 11.
b) The first time that you roll a sum of 5 or 11 is on your 7th
roll.
c) The 3rd time you roll a sum of 5 or 5 is on your 7th
roll.
Solutions from back of textbook:
a) 0.1667
b) 5.58%
c) 3.35%

you roll a fair pair od dice. Find the following.
a.)sum of five or seven
b.)sum of ten
c.)a one on both die at the same time
d.) sum of six or an even number

If you roll a pair of fair dice, what is the probability of : a)
getting a sum of 2? b) getting a sum of 8? c) getting a sum of
13?

Consider an experiment where we roll 7 fair 6-sided dice
simultaneously (the results of the dice are
independent from each other).
(a) What is the probability that exactly 3 of the dice are greater
than or equal to 5?
(b) Suppose now that each of the 7 6-sided dice are weighted the
same such that the probability of
rolling a 6 is 0.5, and every other side that is not a 6 has equal
probability of being rolled. If we...

Suppose that you roll a pair of 24-sided dice (with the sides
numbered 1-24) a total of 299 times. What is the probability that
you will get a sum of 47 at least twice?

Consider the experiment of rolling two standard (six-sided) dice
and taking their sum. Assume that each die lands on each of its
faces equally often. We consider the outcomes of this experiment to
be the ordered pairs of numbers on the dice, and the events of
interest to be the different sums.
Write out the generating function F(x) for the sums of the dice,
and show how it factors into the generating functions for the
individual die rolls.
Use F(x)...

Consider the following game. You roll two fair dice. If you roll
a sum of 8, you win $9. Otherwise, you lose $1. Find the expected
value (to you) of the game.
A) $0.39
B) $1.25
C) $0.09
D) $0.00
E) -$0.50

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