Week 09 Homework
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MA4102: Business Mathematics 1: Week 9 Homework EG1 An experiment consists of two trials. The first is tossing a coin and observing a head or a tail; the second is rolling a die and observing a 1, 2, 3, 4, 5, or 6. Construct the sample space. Write out the subsets of the sample space for the following events: (a) the coin came up a head, (b) the number was an even number. EG2 Fifty voters cast a secret ballot in an plebiscite asking them if they are in favour of property tax. Assuming all votes are valid, construct the sample space. EG3 On her way to work on a rainy day, Ruth’s personal judgment is she that he is twice as likely to get caught in traffic (T ) than have a clear run (C ). What values should be assigned to P (T ) and P (C )? EG4 A fair coin is tossed three times, and heads (H ) or tails (T ) is noted each time. What is the probability of (a) A = {exactly one head in three tosses}? (b) B = {at least one head in three tosses}? (c) C = {at most one head in three tosses}? AH1 In University of Limerick, male students engage in recreational sports in the following proportions: soccer (S) 20%, hurling (H) 30%, both soccer and hurling 5%. What is the probability that a student selected at random will: (a) play soccer or hurling or both? (b) play neither sport? EG5 The probability that a randomly consumer has tried Tayto crisps (T) is 0.5, has tried Pepsi (P) is 0.6, and has tried both Tayto and Pepsi is 0.2. Find the following probabilities: (a) P(has not tried Pepsi) (b) P(has tried neither Tayto nor Pepsi) (c) P(has tried Tayto but not Pepsi) (d) P(has tried Pepsi but not Tayto) (e) P(has tried Tayto or Pepsi or both). EG6 Suppose the event A is “Alice gets promoted this year”, B is “Bill gets promoted this year”, and C is “Chris gets promoted this year”. Suppose that P (A)=0.15, P (B)=0.25, P (C )=0.3 and that all three events are independent. Find the probability that: (a) All three get promoted this year. (b) Alice and Bill get promoted this year but Chris does not. (c) None of the three gets promoted this year. AH2 The probability that a consumer would make a claim on their house insurance last year was 0.033. The probability that a consumer would claim on their car insurance last year was 0.168. The probability that a consumer would claim on both their house and car insurance was 0.004. What is the probability that a consumer would claim on their car insurance during the year given that the consumer had claimed on their house insurance during the year? AH3 A machine is composed of two components, A and B, which function or fail independently of one another. The machine works only if both components work. The probability that component A works is 0.98 and the probability that component B works is 0.95. What is the probability that the machine works? AH4 The chance that a factory’s sprinkler system will fail is 20%. The chance that its’ alarm system will fail is 10% and the chance that they both will fail at the same time is 4%. What is the probability that at least one will work? AH5 A manufacturer of calculators buys integrated circuits from suppliers A, B, and C. 50% of the circuits come from A, 30% from B, and 20% from C. 1% of the circuits supplied by A are defective, 3% of the circuits supplied by B are defective, and 4% of the circuits supplied by C are defective. A circuit is selected at random and found to be defective. What is the probability that it came from B?
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Transcript of Week 09 Homework
MA4102: Business Mathematics 1: Week 9 Homework
EG1 An experiment consists of two trials. The first is tossing a coin and observing a head or a tail; thesecond is rolling a die and observing a 1, 2, 3, 4, 5, or 6. Construct the sample space. Write out the subsets ofthe sample space for the following events: (a) the coin came up a head, (b) the number was an even number.
EG2 Fifty voters cast a secret ballot in an plebiscite asking them if they are in favour of property tax.Assuming all votes are valid, construct the sample space.
EG3 On her way to work on a rainy day, Ruth’s personal judgment is she that he is twice as likely to getcaught in traffic (T ) than have a clear run (C). What values should be assigned to P (T ) and P (C)?
EG4 A fair coin is tossed three times, and heads (H) or tails (T ) is noted each time. What is the probabilityof (a) A = {exactly one head in three tosses}? (b) B = {at least one head in three tosses}?(c) C = {at most one head in three tosses}?
AH1 In University of Limerick, male students engage in recreational sports in the following proportions:soccer (S) 20%, hurling (H) 30%, both soccer and hurling 5%. What is the probability that a student selectedat random will: (a) play soccer or hurling or both? (b) play neither sport?
EG5 The probability that a randomly consumer has tried Tayto crisps (T) is 0.5, has tried Pepsi (P) is 0.6,and has tried both Tayto and Pepsi is 0.2. Find the following probabilities: (a) P(has not tried Pepsi)(b) P(has tried neither Tayto nor Pepsi) (c) P(has tried Tayto but not Pepsi)(d) P(has tried Pepsi but not Tayto) (e) P(has tried Tayto or Pepsi or both).
EG6 Suppose the event A is “Alice gets promoted this year”, B is “Bill gets promoted this year”, and C is“Chris gets promoted this year”. Suppose that P (A) = 0.15, P (B) = 0.25, P (C) = 0.3 and that all threeevents are independent. Find the probability that:(a) All three get promoted this year.(b) Alice and Bill get promoted this year but Chris does not.(c) None of the three gets promoted this year.
AH2 The probability that a consumer would make a claim on their house insurance last year was 0.033. Theprobability that a consumer would claim on their car insurance last year was 0.168. The probability thata consumer would claim on both their house and car insurance was 0.004. What is the probability that aconsumer would claim on their car insurance during the year given that the consumer had claimed on theirhouse insurance during the year?
AH3 A machine is composed of two components, A and B, which function or fail independently of oneanother. The machine works only if both components work. The probability that component A works is 0.98and the probability that component B works is 0.95. What is the probability that the machine works?
AH4 The chance that a factory’s sprinkler system will fail is 20%. The chance that its’ alarm system willfail is 10% and the chance that they both will fail at the same time is 4%. What is the probability that atleast one will work?
AH5 A manufacturer of calculators buys integrated circuits from suppliers A, B, and C. 50% of thecircuits come from A, 30% from B, and 20% from C. 1% of the circuits supplied by A are defective, 3%of the circuits supplied by B are defective, and 4% of the circuits supplied by C are defective. A circuit isselected at random and found to be defective. What is the probability that it came from B?
