Problem 1. (1 point) One die is rolled. List the outcomes comprising the following events: (make sure you use the correct notation with the set braces , put a comma between each outcome, and do not put a space be- tween them): (a) event the die comes up at most 2 answer: (b) event the die comes up even answer: (c) event the die comes up 3 answer: Answer\") submitted: 0 no response 0 no response 0 no response submitted: (incorrect) recorded: (incorrect) Problem 2. (1 point) Determine the size of the sample space that corresponds to the experiment of tossing a coin the following number of times: (a) 2 times Answer: (b) 8 times Answer: (c) n times Answer: Answenfs) submitted: 0 no response 0 no response 0 no response submitted: (incorrect) recorded: (incorrect) Problem 3. (1 point) Determine whether the following number can possibly be proba- bility. Write "YES\" for yes and "NO\" for no. (without quotations) (a) 0.8 answer: (b) 0 answer: (c) -2.1 answer: (d) 1 answer: (e) % answer: (f) 3.1 answer: Answerfs) s ubmitted: 0 no response no response no response no response no response no response submitted: (incorrect) recorded: (incorrect) Problem 4. (1 point) Consider a sample space of three outcomes A,B,and C. Which of the following represent legitimate probability models? a A. P(A)=0.5, P(B)=0.2, P(C)=0.5 o B. P(A)=0.3, P(B)=0.1,P(C)=0.5 o C. P(A)=1, P(B)=l, P(C)=l o D. P(A)=0.l, P(B)=O.2, P(C)=0.7 o E. P(A)=0.l, P(B)=0.9, P(C)=O Answerfs) submitted: 0 no response submitted: (incorrect) recorded: (incorrect) Problem 5. (1 point) Problem 8. (1 point) A basketball player makes 145 out of 190 free throws. We would Three coins are tossed. Find the probability of tossing each of the estimate the probability that the player makes the next free throw following events: to be Answer(s) submitted: 1. Three heads. . no response Answer: submitted: (incorrect) recorded: (incorrect) 2. Two heads and a tail. Answer: Problem 6. (1 point) A jar contains 4 white, 12 blue, and 15 red marbles. If one marble 3. At least one tail. is drawn at random from the jar, find the probability that: Answer: 1. the marble is white or blue. 4. At least two heads. Answer: Answer: 2. the marble is white or red. Answer(s) submitted: Answer: . no response no response 3. the marble is blue or red. . no response Answer: . no response submitted: (incorrect) Answer(s) submitted: recorded: (incorrect) no response . no response . no response submitted: (incorrect) recorded: (incorrect) Problem 7. (1 point) Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likeli- hood given. Type the correct letter in each box. You must get all Problem 9. (1 point) of the answers correct to receive full credit. Suppose that X is an event, and that P(X ) = 0.38. What is P(X) (i.e. the probability that X will not occur)? 1. This event is very unlikely to happen, but it will occur once in a while in a long sequence of trials. 2. This event is impossible. It will never happen. Answer = 3. This event will occur more often than not. 4. This event is very likely to occur. Answer(s) submitted: . no response A. 0 B. 0.92 submitted: (incorrect) C. 0.58 recorded: (incorrect) D. 0.02 Answer(s) submitted: . no response . no response . no response . no response submitted: (incorrect) recorded: (incorrect)Problem 10. (1 point} Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of the students: Problem 11. (1 point) Two sixsided dice are rolled (one red and one green). Some pos sibilities are (Red=l ,Green=5) or (Red=2,Green=2) etc. (a) How many total possibilities are there?I Language Spanish French German |All Others N511: the rest of the questions, we will assume that the dice are fair Probability 0.25 0.08 0.04 | 0.01 011511 thpt all of the possibilities in (a) are equally likely. (a) What is the probability that a randomly chosen student is, in fact, studying a language other than English? ANSWER _ (b) What is the probability that a randomly chosen student is studying French, German, or Spanish? ANSWER _ (c) What is the probability that a randomly chosen student is studying a language besides English, but not German? ANSWER _ Answerf's) submitted: 0 no response 0 no response 0 no response submitted: (incorrect) recorded: (incorrect) Generated by DWeBWarK. http:tfwebwmk.maa.org. Mathematical Association of America (b) What is the probability that the sum on the two dice comes out to be 12? (c) What is the probability that the sum on the two dice comes out to be 8? (d) What is the probability that the numbers on the two dice are equal? Answerfs) submitted: a no response . no response o no response o no response submitted: (incorrect) recorded: (incorrect)