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A pair of dice is rolled five times. What is the probability the first two results are “sevens” and the others are not?
.
David, Mary, Joan, Hal, Sharon, and Wayne take an exam in their probability course. Their probabilities of making 90 percent or more are
respectively. Assume these are independent events. What is the probability three or more, four or more,five or more make grades of at least 90 percent?
P = 0.01*[72 83 75 92 65 79];y = ckn(P,[3 4 5])y = 0.9780 0.8756 0.5967 Two independent random numbers between 0 and 1 are selected (say by a random number generator on a calculator). What is the probability the first is no greaterthan 0.33 and the other is at least 57?
Helen is wondering how to plan for the weekend. She will get a letter from home (with money) with probability 0.05. There is a probability of 0.85 that she willget a call from Jim at SMU in Dallas. There is also a probability of 0.5 that William will ask for a date. What is the probability she will get money and Jim will not call orthat both Jim will call and William will ask for a date?
letter with money, call from Jim, William ask for date
P = 0.01*[5 85 50];minvec3
Variables are A, B, C, Ac, Bc, CcThey may be renamed, if desired.
pm = minprob(P);p = ((A&Bc)|(B&C))*pm'
p = 0.4325 A basketball player takes ten free throws in a contest. On her first shot she is nervous and has probability 0.3 of making the shot. She begins to settle down and probabilitieson the next seven shots are 0.5, 0.6 0.7 0.8 0.8, 0.8 and 0.85, respectively. Then she realizes her opponent is doing well, and becomes tense as she takes the last two shots, withprobabilities reduced to 0.75, 0.65. Assuming independence between the shots, what is the probability she will make k or more for
P = 0.01*[30 50 60 70 80 80 80 85 75 65];k = 2:10;
p = ckn(P,k)p =
Columns 1 through 70.9999 0.9984 0.9882 0.9441 0.8192 0.5859 0.3043
Columns 8 through 90.0966 0.0134 In a group there are M men and W women; m of the men and w of the women are college graduates. An individual is picked at random. Let A be the event the individual is a woman and B be the event he or she is a college graduate. Under what condition is the pair independent?
Consider the pair of events. Let , , , and . Under what condition is the pair independent?
(see table of equivalent conditions).
Show that if event A is independent of itself, then or . (This fact is key to an important “zero-one law.”)
. iff or .
Does independent and independent imply is independent? Justify your answer.
% No. Consider for example the following minterm probabilities:
pm = [0.2 0.05 0.125 0.125 0.05 0.2 0.125 0.125];
minvec3Variables are A, B, C, Ac, Bc, Cc
They may be renamed, if desired.PA = A*pm'
PA = 0.5000PB = B*pm'
PB = 0.5000PC = C*pm'
PC = 0.5000PAB = (A&B)*pm' % Product rule holds
PAB = 0.2500PBC = (B&C)*pm' % Product rule holds
PBC = 0.2500PAC = (A&C)*pm' % Product rule fails
PAC = 0.3250 
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