8. 9. 10. 6. An actuary studied the likelihood that different types of drivers would be...
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8. 9. 10. 6. An actuary studied the likelihood that different types of drivers would be involved in at least one collision during one-year period. The results are presented below. Type Of driver Teen Young Adult Midlife Senior percentage of all drivers 8% 16% 45% 31% probability of at least one collision 0.15 0.08 0.04 0.05 a) Find the probability of an accident occurring. b) Find the probability that a teen was involved in an accident given that an accident was reported. 7. The probability that a person with certain symptoms has hepatitis is 0.8. the blood test used to confirm this diagnosis gives positive results for 90% of people with the disease and 5% of those without the disease. A) What is the probability that a person will test positive? B) What is the probability that a person will test negative? C) What is the probability that a person actually has the disease given that the test is positive? D) What is the probability that a person does not have a disease given that the test is negative? THERE Skewed Ciga 4. Draw a ste students on t 136 124 157 156 163 (124) 155 166 171 Take-home with some more problems (SAS part will come next.) 1. A coin is tossed five times. Write the sample space. Assume P(H) = p, assign probability to each outcome. Making a tree will be helpful. Obtain the probability mass function of random variable X = number of heads in an outcome. 2. A jar contains red, blue and green balls such that the probability of drawing a red ball, blue ball and green ball are p, q and r, respectively. Three balls are drawn with replacement. Let the random variables X = no. of red balls, Y = No. of blue balls. Construct a tree for outcomes of the experiment. Y X\ Make a table of probabilities. 3. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} be the sample space. X = {2, 4, 6, 8}, Y = {2, 3, 4, 5, 6), Z = {1, 2, 3, 8, 9}. Find a) XUY b) Xcnyc c) Xcn (YC UZ) b)XnY e) Xc nz c) XC d) yc f) (X nyº) U (Zºnyc) 4. Suppose two fair dice are rolled. Find each probability. a) The first die shows a 2 or the sum of face values is 6 or 7. b) The sum of the face values is 11 or the second die shows a 5. c) The sum of the face values is greater than 3. njnews 5. Susan is a college student who receives heavy sweaters from her aunt at the first sign of cold weather. Susan has determined that the probability that a sweater is the wrong size is 0.47, the probability that it is a loud color is 0.59, and the probability that it is both the wrong size and wrong color is 0.31. a) Find the probability that the sweater is the correct size and not a loud color. b) Find the probability that the sweater is the correct size or is not loud color. 8. Given P(E) = 0.4, P(F) = 0.5 and P(EUF) = 0.7. Find P(E|F) and P(FIE). I am expecting a good discussion during class. Correct answer will not be given but the process will be given. Read and attempt at least. M 8. 9. 10. 6. An actuary studied the likelihood that different types of drivers would be involved in at least one collision during one-year period. The results are presented below. Type Of driver Teen Young Adult Midlife Senior percentage of all drivers 8% 16% 45% 31% probability of at least one collision 0.15 0.08 0.04 0.05 a) Find the probability of an accident occurring. b) Find the probability that a teen was involved in an accident given that an accident was reported. 7. The probability that a person with certain symptoms has hepatitis is 0.8. the blood test used to confirm this diagnosis gives positive results for 90% of people with the disease and 5% of those without the disease. A) What is the probability that a person will test positive? B) What is the probability that a person will test negative? C) What is the probability that a person actually has the disease given that the test is positive? D) What is the probability that a person does not have a disease given that the test is negative? THERE Skewed Ciga 4. Draw a ste students on t 136 124 157 156 163 (124) 155 166 171 Take-home with some more problems (SAS part will come next.) 1. A coin is tossed five times. Write the sample space. Assume P(H) = p, assign probability to each outcome. Making a tree will be helpful. Obtain the probability mass function of random variable X = number of heads in an outcome. 2. A jar contains red, blue and green balls such that the probability of drawing a red ball, blue ball and green ball are p, q and r, respectively. Three balls are drawn with replacement. Let the random variables X = no. of red balls, Y = No. of blue balls. Construct a tree for outcomes of the experiment. Y X\ Make a table of probabilities. 3. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} be the sample space. X = {2, 4, 6, 8}, Y = {2, 3, 4, 5, 6), Z = {1, 2, 3, 8, 9}. Find a) XUY b) Xcnyc c) Xcn (YC UZ) b)XnY e) Xc nz c) XC d) yc f) (X nyº) U (Zºnyc) 4. Suppose two fair dice are rolled. Find each probability. a) The first die shows a 2 or the sum of face values is 6 or 7. b) The sum of the face values is 11 or the second die shows a 5. c) The sum of the face values is greater than 3. njnews 5. Susan is a college student who receives heavy sweaters from her aunt at the first sign of cold weather. Susan has determined that the probability that a sweater is the wrong size is 0.47, the probability that it is a loud color is 0.59, and the probability that it is both the wrong size and wrong color is 0.31. a) Find the probability that the sweater is the correct size and not a loud color. b) Find the probability that the sweater is the correct size or is not loud color. 8. Given P(E) = 0.4, P(F) = 0.5 and P(EUF) = 0.7. Find P(E|F) and P(FIE). I am expecting a good discussion during class. Correct answer will not be given but the process will be given. Read and attempt at least. M
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Question 6 Column A Column B AB of all the drivers Prob of at least one collision 008 015 0012 016 0... View the full answer
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