Question 1 Score on last try: 3 of 8 pts. See Details for more. Next question Get a similar question |You can retry this question below A garage has a letter-keypad lock with the nine letters A,B,C, D,E,F,G, H,I. The keypad can be programmed with a 3 or 5-letter code to open the garage. 1. Suppose each letter can be used more than once, how many 3-letter codes are possible if: a) there are no restrictions? 729 b) the letters "A" and "B" cannot be used? | 343 c) the letter "D" must be used? 81 d) the same letter is repeated three times? 9 2. If each letter cannot be repeated, how many 5-letter codes are possible if: a) the letters "A" and "B" cannot be used? 16,807 X b) the letter "D" must be used? 59,047 X c) the order in which the they are entered does not matter? | 6561 d) the order of entries does not matter and "G" must be used? | 40824Question 2 Score on last try: 5 of 10 pts. See Details for more. > Next question Get a similar question You can retry this question below A four or five-digit PIN is to be selected from the seven digits 0,1,2,3,4,5,6. 1. How many 4-digit PINs are possible if: a) all 4 digits are the same? e.g. 4-4-4-4 2394 b) no digit can be repeated? 840 c) any digit can be repeated? 2401 d) the first 2 digits must be different digits and the last 2 digits must be the same, but none of the first 2 digits can be used in the last 2? 1050 2. Suppose any digit can be repeated, how many 4-digit PINs are possible if each PIN: a) must end with "0"? 343 b) must not start with "6"? 2058 c) must neither start with "4" nor end with "4"? 1764 3. Suppose no digit can be repeated, how many 5-digit PINs are possible if each PIN: a) must end with "0"? 120 X b) must not start with "6"? 720 X c) must neither start with "4" nor end with "4"? 720 X. Question 3 In a group of 32 employees, 13 take public transit while 11 drive to work. 10 employees from this group are to be selected for a study. Note: Employees either only take the public transit, only drive to work, or do neither. 1. How many different groups of 10 employees can be selected from the 32 employees? How many of the possible groups of 10 employees will: 2. consist only of employees that either take public transit or drive to work? 3. consist entirely of those that take public transit? 4. consist entirely of those that drive to work? 5. not include anyone that takes public transit? 6. not include anyone that drives to work? 7. consist of at least one person that takes public transit? 8. consist of at least one person that drives to work? 9. consist of 5 people that take the transit and 5 that drive to work? 10. consist exactly of 4 people that take the transit and exactly 3 that drive to work?*Question 4 Score on last try: 1 of 8 pts. See Details for more. > Next question Get a similar question You can retry this question below The probability that laptop A will rise in price is 0.66 while the probability that laptop B will rise in price is 0.59. The probability of both laptops rising in price is 0.49. A = laptop A will rise in price B = laptop B will rise in price Report numeric answers to 2 decimal places. Do not convert to percent. 1. Use the given information to complete the following probability table. A and B represent the complements of events A and B respectively. B B Total A 0.49 0.27 * 0.76 x A 0.20 x 0.04 x 0.24 x Total 0.69 X 0.31 x 1.00 2. What is the probability that a) laptop B will not rise in price? 0.41 b) only laptop A will rise in price? 0.27 x c) at least one laptop will rise in price? | 0.96 x d) both laptops will not rise in price? |0.04 x e) only one laptop will rise in price (not both)? |0.47 x () no more than one laptop will rise in price? 0.47 x 3. a) Are A and B mutually exclusive? Why? No. They cannot occur at the same. VX b) Are A and B independent? Why? Yes. Occurrence of one does not affect the probability of the other. V x. Question 5 The following joint frequency distribution table shows responses from a sample of 210 unionized employees on how their union president handled a recent labour action. Employees were categorized by age group and by their level of approval. Age Group Approve Disapprove Indifferent Total under 25 9 38 29 76 25 to 40 19 33 5 57 over 40 23 28 26 77 Total 51 99 60 210 Report answers accurate to at least 4 decimal places. 1. What is the probability that a randomly selected employee: a) did not disapprove? b) was in the 25 to 40 age group and was indifferent? c) was not in the 25 to 40 age group and was indifferent? d) was in the over 40 age group or approved? e) was not in the over 40 age group or approved? f) was not over 40 and did not disapprove? 2. Given that an employee was in the under 25 age group, what is the probability that the employee a) was indifferent? b) did not approve? 3. What is the probability of selecting an employee that was in the over 40 age group from a group of employees that a) was indifferent? b) did not disapprove?. Question 6 Use the following Venn diagram to determine the required probabilities. A B 0.23 0.18 0.49 a Round to 3 decimal place where necessary to round. 1. P(A) 2. P(B) = 3. P(A and B) = 4. P(A and B) = 5. P(A and B) = 6. P(A or B) = 7. P( A or B) = 8. P( A and A ) = 9. P(B | A) = 10. P(A | B) =. Question 7 The probabilities of events A and B respectively are given below. P(A) = 0.30 P(B) = 0.20 Do not round answers. 1. If A and B are independent events, then a) P( A and B) = b) P(A or B) = c) P(B | A) = d) P(B and A) = e) P(A and B) = 2. If A and B are mutually exclusive events, then a) P(A and B) = b) P(A or B) = c) P(A | B) = d) P(A and B) = e) P(A and B) =. Question 8 A sports fan group in large city is considering 3 teams (A, B, and C) that could potentially win a championship soon. The probability that team A will win a championship is 0.9 while that of B and C are 0.6 and 0.8 respectively. Assume these events are independent. Hint: Draw a probability tree/tree diagram. Do not round calculation results. What is the probability that 1. all 3 teams will win a championship? 2. none of the 3 teams will win a championship? 3. not all 3 teams will win a championship? 4. only team B will win a championship? 5. only teams A and C will win a championship? 6. only team C will not win a championship? 7. at least one team will win a championship? 8. no more than two teams will win a championship? 9. only one team will win a championship? 10. team A will not win a championship given both B and C win a championship