You are taking two courses during winter session, math and history, and your subjective assessment of your performance is
Event Probability
fail both courses .05
fail math (irrespective of whether or not you fail history as well) .15
fail history (irrespective of whether or not you fail math as well) .08

Let's develop a joint-probability table to analyze this problem (the letters A - H representprobability values. For example, A is the probability of failing both math and history; B is the probability of failing math and passing history; while C is the sum of A and B, and represents the probability of failing math).

fail history pass history row sum
fail math A B C
pass math D E F
column sum G H

a) (3 pts.) What does C + F equal?
b) (3 pts.) What does A + B + D + E equal?
c) (12 pts) What is the probability of failing math only (that is, you fail math but pass history)?
d) (12 pts) What is the probability of passing either course?

The following table summarizes results from the sinking of the Titanic:
Men Women boys Girls
Survived 332 318 29 27
Died 1360 104 35 18
If one of the Titanic passengers is randomly selected, find the probability of getting a woman or someone who didn't

2. For the following table, what is the value of :
a) P(A1)
b) P(B1│A2)
c) P(B2 and A3). Compute this as P(B2)*P(A3│ B2) . In what row and column will you find this answer? Rows are B1 & B2: columns are A1, A2 & A3.
Second Event
First Event
A1 A2 A3 Total
B1 2 1 3 6
B2 1 2 1 4

What are the steps for using the Normal Table to find the following:
a. The Probability steps for (z<-2.65)
b. The Probability (z>-1.55)
c. The Probability (-2.00Probability (1.25

Given the following contingency table:
C D Total
A 10 30 40
B 20 40 60
Total 30 70 100
Find the probability of A and C.
a) 33.3%
b) 10%
c) 25%
Find the probability of A or C
a) 60%
b) 70%
c) 10%
Find the probability of B given C
a) 20%
b) 30%
c) 66.67%

Please refer to the attachment for the Joint ProbabilityTable.
A. If a driver in this city is selected at random, what is the probability that he or she drives less than 10,000 miles per year or has a accident?
B. If a driver in this city is selected at random, what is the probability that he or she drives 10,000 or more

A retail outlet receives radios from three electrical appliance companies. The outlet receives 20% of its radios from A, 40% from B, and 40% from C. The probability of receiving a defective radio from A is .01; from .02; and from C .08.
A. Develop a probability tree showing all marginal, conditional and joint probabilities.

Use the Normal Table to find the following:
a) Probability (z < -2.65)
b) Probability (z > -1.55)
c) Probability (-2.00 < z < 2.25)
d) Probability ( 1.25 < z < 2.40)
Please show the steps you used to get to the answers.

The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
States A1 A2 A3
1 12 -2 8
2 4 10 5
Where: S1 is state of nature 1 A1 is action alternative 1
S2 is state of nature 2 A2 is action alternative 2

A normal population has a mean of 80.0 and a standard deviation of 14.0.
a. Compute the probability of a value between 75.0 and 90.0.
b. Compute the probability of a value 75.0 or less.
c. Compute the probability of a value between 55.0 and 70.0