1)how can two cubical (six sided) dice be labelled using numbers {0,1,2,3,4,5,6}
ID: 3550294 • Letter: 1
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1)how can two cubical (six sided) dice be labelled using numbers {0,1,2,3,4,5,6} so that when the two dice are thrown, the sum has a uniform probability distribution over the integers ( 1,2...12}.The same number can repeat more than once on a face of either die, but each face will come up with the same probability 1/6 when the die is rolled.
2)A test for a disease is 90% reliable, i.e. in 90% of cases of people who have the diease,a positive test result is returned and in 90% of the people who do not have the disease, a negative result is obtained. Suppose that 1% of people are known to have the disease. If a person X takes the test and gets a positive result for the test, what is the probability that X actually has the disease?
3)Alice and Bill flip a fair coin until one of the respective patterns A = HHT or B = HTT appears for the first time (and then the corresponding player wins). Here is a state diagram that indicates how Alice (or Bill) would proceed to a win: the transitions indicate flips of a fair coin (H/T).
Use the state diagram to calculate:
(a) by hand, the exact probability that Alice wins within 5 or fewer coin flips
(b) via a programmed function that takes n 3 as argument and returns the ratio of the probability that Alice wins in exactly n flips to the probability that Bill wins in exactly n flips.
4)Redo problem 3 but this time choose winning patterns A = THH and B = HHT. You will need to draw a state diagram based on these patterns before answering parts (a) and (b) as above.You should be able to reuse the code in p3 if you parmaterize the functions properly
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