1. List the entire sample space for each of the following scenarios. Remember to either declare your variables (let H represent heads, let T represent tails) or to clearly indicate what your shorthand means. Use correct notation. a) Flipping a standard coin (quarter) 3 times (4) b) Rolling a single 3-sided dice 2 times (4) 2. A bartender decides to play a round of cards before he goes home for the evening. The dealer tells him that if he can look at two sample spaces of cards, and draw a Venn Diagram of the situation, he will give him a high five. The Dealer shows him the following sets: Q = Queen K = King J = Jack H = Hearts S = Spades C = Clubs D = Diamonds A = Ace {QH, AS, 7C, KD, 9C, 3S, 7H} {8C, AD, JD, JH, AS, KH, 3H, 3S} The dealer tells him that he can divide by the sample space, or you can divide the cards between black and red to make your drawing. You may use digital software to help with your drawing, or draw it by hand. (4) 3. Maria plays tennis. She wins 67% of the matches she plays. Maria is going to attempt two wins in a row at next week's tournament. A = the event Maria is successful on her first attempt. P(A) = 0.67. B = the event Maria is successful on her second attempt. P(B) = 0.67. Maria tends to win, but often gets tired after playing a match. The probability that she makes the second win | that she made the first win is 0.60. a. What is the probability that she wins twice in a row? (4) b. What is the probability that Maria wins either the first or the second game? (4) c. Are these events mutually exclusive? Prove your response. (4) d. Are these events independent? Prove your response. (4) QMM1233 - Statistics Assignment 3 Due: 11/07/2022 4. A zoo has a population of animals. It has 300 different birds, of whom 80 of which will be moved to a tropical enclosure in the winter. 110 can remain in their enclosures, and don't need to be moved. The remainder are being released after being successfully rehabilitated. Out of the birds that must be moved into a tropical enclosure, 30 are red in colour. Of the birds that can remain in their enclosures, only 20 are red. Lastly, of the birds being released, only 1 is red. What is the probability that a red bird is being moved into a tropical enclosure? (4) 5. A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.45, P(D) = 0.50 and P(D|B) = 0.30. a. Find P(B D). (2) b. Find P(B D). (2) c. What is the probability that a student does not select a book nor a DVD? (2) 6. Suppose a study of records the number of people who regularly read books, as well as recently received a prescription for glasses in the past year: Received a Prescription for Glasses Did Not Receive a Prescription for Glasses Total Reads at 1 or more books a week 88 22 110 Does not read any books 38 65 103 Total 126 87 213 a) Find P(reads one or more books per week). (4) b) Find P(a reader had no need for prescription glasses in the last year). (4) c) Find P(does not read any books received a prescription for glasses). (4) d) Find P(reads books received a prescription for glasses). (4) 7. Given the following set of data, construct a histogram by hand. You may select the number of bars you use, but ensure your width is consistent across your drawing. Remember to include appropriate labels for your chart. Use either frequency or relative frequency in your chart. (10) Decibel Activity in an Unused Mineshaft (dB) 0, 0, 1, 3, 2, 6, 7.4, 2, 0, 3, 1, 9, 7, 7, 4 Hint: I used 4 bars in my sample drawing, ranging from 0 - 12 on my x-axis. You may proceed any way you wish, this is just to give you a possible idea.