1.4-13 Tn the gambling game "craps" a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up-sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2, 3, or 12. If the sum is 4, 5, 6, 8, 9, or 10, that number is called the bettor's "point." Once the point is established, the rule is, If the bettor rolls a 7 before the "point," the bettor loses; hut if the "point" is rolled before a 7, the bettor wins.
(a) List the 36 outcomes in the sample space for the roll of a pair of dice. Assume that each of them has a probability of 1/36.
(b) Find the probability that the bettor wins on the first roll. That is, fInd the probability of rolling a 7 or ii, P(7 or 11).
(c) Given that 8 is the outcome on the first roll, find the probability that the bettor now rolls the point 8 before rolling a 7 and thus wins. Note that at this stage in the game the only outcomes of interest are 7 and 8. Thus find P(8 | 7 or 8).
(d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 | 7 or 8). Show that this probability is (5/36)(5/11).
(e) Show that the total probability that a bettor wins in the game of craps is 0.49293.
HINT: Note that the bettor can win in one of several mutually exclusive ways: by rolling a 7 or ii on the first roll or by establishing one of the points 4, 5, 6. 8, 9, or 10 on the first roll and then obtaining that point before a 7 on successive rolls.

Conditional probability is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

I have been struggling with theses two following problems:
illustration: age a(0.00%) b(0.01-0.9%) c(>_0.10%)
d 0-19 142 7 6 155
e 20-39 47 8 41 96
f 40-59 29 8 77

Attached is a table showing the prevalence of Alzheimer's disease.
Suppose an unrelated 77 year old man, 76 year old woman, and 82 year old woman are selected from a community.
1. What is the probability that all three of these individuals have Alzheimer's disease?
2. What is the probability that at least one of t

Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for
i >= 0, j >= 0, and i + j < 4. Determine
a) the marginal probability mass function of X
b) the probability mass function of Y
c) the conditionalprobability mass function of X given Y = 0
d) the probability mass function of Z = X + Y

A medical test for malaria is subject to some error. Given a person who has malaria, the
probability that the test will fail to reveal the malaria is 0.06. Given a person who does not
have malaria, the test will correctly identify that the person does not have malaria with
probability 0.91. In a particular area, 20% of the

What is the probability that probability that a randomly selected moviegoer attend the romantic comedy? See attached file for full problem description.

The probability of having disease X in the general population is only .05. The Sagman Test is a newly discovered method for early detection. Of those who have disease X, the test indicates the disease for 90% of them. Of those who do not have the disease, the test indicates no disease for 90% of them. Is the test a good predicto

A pollster wishes to obtain information on intended voting behavior in a two party system and samples a fixed number (n) of voters. Let X_1 ..., X_n denote the sequence of independent Bernoulli random variables representing voting intention, where E(X_l) = p, i = 1, ..., n
(a) Suppose the number of voters n is fixed, compute

Estimates for the prevalence of Alzheimer's disease provided by an observational study are listed below:
Prevalence of Alzheimer's disease (cases per 100 individuals)
Age-group Males Females
65-69 1.3 0.5
70-74 3.3 2.1
75-79 4.9 3.8
80-84 7.5 8.2