course Mth 151 sorry so late Ϻݳb敛]ʂassignment #009
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14:10:26 `questionNumber 90000 `q001. Note that there are 5 questions in this assignment. What is the probability that on two rolls of a fair die, we obtain exactly two 3's?
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RESPONSE --> The probabilityis 1/6 1/6* 1/6= 1/36 confidence assessment: 3
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14:11:38 `questionNumber 90000 `q002. What is the probability that on three rolls of a fair die, we obtain exactly two 5's?
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RESPONSE --> 1/6* 1/6 *5/6= 5/216 3*5/216 =15/216 confidence assessment: 3
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14:12:59 `questionNumber 90000 `q003. What is the probability that on six rolls of a fair die, we obtain exactly two 5's?
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RESPONSE --> 1/6 * 1/6 * 5/6* 5/6 *5/6 * 5/6= 1/6^2 * 5/6 ^4 confidence assessment: 1
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14:14:15 `questionNumber 90000 `q004. If we let p stand for the probability of getting a 5 on a roll of a die and q for the probability of not getting a 5 on a roll, then how would we expressed a probability of getting exactly r 5's on n rolls?
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RESPONSE --> P = 5 and Q= not r=? confidence assessment: 0
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14:19:56 `questionNumber 90000 `q005. Explain why, if p is the probability of getting a 5 on a single roll of a die, it follows that the probability q of not getting a 5 is q = 1-p. How would we therefore express the formula C(n, r) * p^r * q^(n-r) only in terms of p?
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RESPONSE --> ? confidence assessment: o
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|~z֩ assignment #010 010. Expectation Liberal Arts Mathematics II 03-29-2008
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16:10:00 `questionNumber 100000 `q001. Note that there are 9 questions in this assignment. In a certain lottery the probability of winning $100 is .005, the probability of winning $1000 is .0002 and the probability of winning $10,000 is .00001. Otherwise you win nothing. What is the probability of winning nothing?
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RESPONSE --> .005+ .0002 +.00001 = .00521 1-.00521 =.99479 is the prob.of winning nothing confidence assessment: 3
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16:12:51 `questionNumber 100000 `q002. In the same lottery , where the probability of winning $100 is .005, the probability of winning $1000 is .0002 and the probability of winning $10,000 is .00001, if you bought a million tickets how many would you expect to win the $100 prize? How many would you expect to win the $1000 prize? How many would you expect to win the $10,000 prize?
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RESPONSE --> $100 winnings is .005 *1,000,000=5,000 $1000 winnings is .0002*1,000,000= 200 $10,000 winnings is .00001 *1,000,000 = 10 confidence assessment: 3
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16:16:35 `questionNumber 100000 `q003. In the lottery of the preceding problem, if you were given a million tickets how much total money would you expect to win?
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RESPONSE --> $100=5000 times=500,000 $1000= 200 times=200,000 $10,000= 10 times= 100,000 500,000 +200,000 +100,000= 800,000 winnings confidence assessment: 3
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16:17:48 `questionNumber 100000 `q004. In the lottery of the preceding problem, if you bought a million tickets for half a million dollars would you most likely come out ahead?
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RESPONSE --> Yes the probability of comeing out ahead is good. A million ticket winnings is 800,000 confidence assessment: 2
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16:19:08 `questionNumber 100000 `q005. In the lottery of the preceding problem, how much would you expect to win, per ticket, if you bought a million tickets? Would the answer change if you bought 10 million tickets?
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RESPONSE --> 800,000 / 1,000,000= .80 8,000,000 / 1,000,000= .80 per ticket confidence assessment: 2
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16:20:39 `questionNumber 100000 `q006. If we multiply $100 by the probability of winning $100, $1000 by the probability of winning $1000, and $10,000 by the probability of winning $10,000, then add all these results, what is the sum? How does this result compare with the results obtained on previous problems, and why?
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RESPONSE --> $100* .005+ $1000* .0002 + $10,000 *.00001=.50 +.20 +.10= .80 confidence assessment: 3
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16:22:58 `questionNumber 100000 `q007. The following list of random digits has 10 rows and 10 columns: 3 8 4 7 2 3 0 8 3 9 1 8 3 7 3 2 9 1 0 3 4 3 3 0 2 1 4 9 8 2 4 3 4 9 9 2 0 1 3 9 8 3 4 1 3 0 5 3 9 7 2 4 7 4 5 3 7 2 1 8 3 6 9 0 2 5 9 5 2 3 4 5 8 5 8 8 2 9 8 5 9 3 4 6 7 4 5 8 4 9 4 1 5 7 9 2 9 3 1 2. Starting in the second column and working down the column, if we let even numbers stand for 'heads' and odd numbers for 'tails', then how many 'heads' and how many 'tails' would we end up with in the first eight flips? Answer the second question but starting in the fifth row and working across the row. Answer once more but starting in the first row, with the second number, and moving diagonally one space down and one to the right for each new number.
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RESPONSE --> The 2nd col,down is HHTTTHHT the 5th row, across is HTHTTHTT 1st row, and 2nd# is HTHTHTTH confidence assessment: 3
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16:25:19 `questionNumber 100000 `q008. Using once more the table 3 8 4 7 2 3 0 8 3 9 1 8 3 7 3 2 9 1 0 3 4 3 3 0 2 1 4 9 8 2 4 3 4 9 9 2 0 1 3 9 8 3 4 1 3 0 5 3 9 7 2 4 7 4 5 3 7 2 1 8 3 6 9 0 2 5 9 5 2 3 4 5 8 5 8 8 2 9 8 5 9 3 4 6 7 4 5 8 4 9 4 1 5 7 9 2 9 3 1 2 let the each of numbers 1, 2, 3, 4, 5, 6 stand for rolling that number on a die-e.g., if we encounter 3 in our table we let it stand for rolling a 3. If any other number is encountered it is ignored and we move to the next. Starting in the fourth column and working down, then moving to the fifth column, etc., what are the numbers of the first 20 dice rolls we simulate? If we pair the first and the second rolls, what is the total? If we pair the third and fourth rolls, what is the total? If we continue in this way what are the 10 totals we obtain?
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RESPONSE --> The 4th col., down is 7,7,0,9,1,4,0,5,6,7 the 5ht col. is 2,3,2,9,3,5,2,8,7,9 ? confidence assessment: 0
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16:25:44 `questionNumber 100000 `q009. According to the results of the preceding question, what proportion of the totals were 5, 6, or 7? How do these proportions compare to the expected proportions?
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RESPONSE --> confidence assessment: 0
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