12 Jul Math 183 HW3, Name: PID:1. Suppose you roll a fair
Math 183 HW3, Name: PID:1. Suppose you roll a fair, six-sided die (labeled 1 6) twice.a. Find the probability the results of your rolls match. [WISE] (See the lecture slides for anexplanation of WISE.)b. Find the probability the result on your second roll is at least 3 more than the result on yourrst roll.c. Find the probability that your two rolls will display both a prime number and a compositenumber. Note that 1 is neither prime nor composite. [WISE]12. In each problem below, you are given two events. You must decide if the events are disjoint ornot disjoint. After this, decide if the events are independent or dependent. Explain your reasoning.a. You pick a random UCSD student. A is the event the student is in Muir College. B isthe event the student is in Sixth College.b. You roll a fair die labeled 1 10. A is the event the result is divisible by 3. B is the event theresult is divisible by 6.c. In planet Yoshi, 15% of animals eat mushrooms but not shells. 10% eat both mushrooms andshells. 40% eat shells. Choose a random animal. A is the event the animal eats mushrooms. B isthe event the animal eats shells. [VIZ] (Note: VIZ means to include some sort of visualization thathelps solve the problem. e.g., Venn diagram, contingency table, tree diagram, etc.)23. On May 29, 2019, Twitch streamer DGR posted a video about a Super Mario Maker 1 levelthat he claimed had a 1 in 7.5 million chance of being completed. Your goal is to watch the video,understand how the level works, and check his math. (Note: Super Mario Maker 2 came out inJune 2019 and is NOT the setting for this question.)a. Explain the steps that lead to Mario dying in this level. What happens rst? Then what?Then what? etc.b. When a Magikoopa’s magic hits a question-mark block, it randomly turns it into a item fromthe game. How many di erent items are possible from a single question mark block? (Google OK.)c. If the question-mark block becomes a coin, what is the probability it goes right? (Google OK.)d. Calculate the exact probability Mario lives and compare with DGR’s claim. [WISE]34. Suppose you have a bag with 7 balls: 3 red, 2 white, and 2 blue. You plan to randomly choose3 balls, but will put back each ball as you choose it, so the bag always has 7 balls when you arechoosing. (If we didn’t nish the slides for lecture 4, you’ll want to study these before beginningproblems 4 and 5.)a. What name do we give to this way of choosing balls?b. What is the probability of drawing 3 white balls? [WISE]c. What is the probability of drawing three balls whose colors match? [WISE]d. What is the probability of getting exactly two red balls? [WISE]45. You plan to repeat the experiment of question 4, but this time, you will not return the balls tothe bag as you pick them out. We explore the same questions.a. What name do we give to this way of choosing balls?b. What is the probability of drawing 3 white balls?c. What is the probability of drawing three balls whose colors match? [WISE]d. What is the probability of getting exactly two red balls? [WISE]5
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