Round your answers to four decimal places for binomial and hypergeometric calculations and 2 decimal places for the rest of the calculations 1) The following spinner was spun 20 times. What is the probability of spinning C seven times? [2 marks] 2) A company survey results shows that 24% of employees are vegans. 30 employees were surveyed. What is the probability that 5 employees are vegan? [2 marks] 3) A snack bag contains 7 bags of potato chips and 10 bags of popcorn. Six bags are picked at random from this box without replacement. What is the probability that 2 of these bogs are potato chip bags? [2 marks] A committee of 5 is to be randomly selected from a small company employing 6 Engineers, 5 Accountants, 8 Consultants, and 4 Lawyers. What is the probability of having 2 engineers on the committee? [2 marks] 5) Two dice were rolled 30 times. What is the probability of getting a sum greater than 8, seven times? [2 marks]1} Consider the game of spinning the spinner shown to the right. If you spin Red, you win 40 points. If you spin Yellow. you win 10 points. Ifyou spin Blue. you lose 3 points. Ifyou spin Purple. you lose T points. I] Develop a probability distribution fortbe points earned per spin. [2 marks] b} What is the expected number of points per spin?[l marks] I} Consider the game of spinning the equal segment spinner to the right. If you spin an odd number you win that number of points but if you spin an even number you lose 4 times that number. . What is the expected value of this game? Is this a fair game? justify your answer [3 marks] 3} You spin the following spinner ll] times. [4 marks] a} How many times do you expect it to land on WIN? b] What is the probability of spinning L033 4 times? o} What is the probability of spinning WIN 2 times? 1) Dan bought a box with 90 USB drives for his company. The defect rate for this USB drives brand is 1.8%. What is the probability that at least two of these USB drives are defective? [2 marks] 2) A committee of 10 is to be selected from 7 Biologists, 15 Chemists, and 16 Mathematicians. What is the probability that the number of Mathematicians on the committee are triple the Biologist? [2 marks] 3) A bag contains 12 red marbles, 10 orange, and 11 yellow marbles. 8 marbles are selected at random from this bag, what is the probability that at most 6 are orange? [2 marks] 4) The following two independent spinners were spun simultaneously 10 times. What is the probability of getting 1 on both three times? [2 marks] 5) A committee of 6 is to be randomly selected from 7 Mathematicians and X Chemists. If the expected number of Mathematicians on the committee is 1.4, what is x ? [2 marks]