1] A die is tossed twice. What is the probability that the sum of the two tosses is an even number? 2] A die is cast three times. What is the probability that the sum of all three tosses is at least six? 3] Let the sample space S = {0, L 2, 3, 4, 5, 6, TI", 8, 9} - Given events A = {EL 2' 5. '5, 9} . B = {1, 2, 5, T, 9}, and C: = {1, 5, r3, 8}, determine the set [A or (B and [3-]. 4] Roll a die. If it lands 3 or 5 roll it one more time and then stop. Otherwise, ip a coin. If the coin lands tails then stop. If it lands heads. roll the die again and stop. List the entire sample space (all possible outcomes} for this experiment. 5) An um contains blue chips and red chips. If the odds of selecting a blue chip at random are 4: 9. what is the probability of selecting a blue chip? 6] An urn contains green chips and yellow chips. It the probability of selecting a green chip is 40%, what are the odds of selecting a green chip? T) In a survey of 43 college students. 30 have a laptop, 22 have a smartphone, and 40 have a laptop or a smartphone [or both). What percentage of students surveyed had both? 3) In a survey of 450 university professors. it was found that 30 held a graduate degree in Engineering, 25 in Math, and 20 in Physics. 3 held graduate degrees in Engineering and Physics, 5 in Math and Physics, and 4 in Engineering and Math. Additionally, 2 were found to hold graduate degrees in all three disciplines. How many professors held exactly one graduate degree in any of these three disciplines? 9] The probability of a randomly chosen driver making a phone call during any given trip is 25%. The probability of a randomly chosen driver running a red light during any given trip is 12%. The probability of doing at least one or the other [or both} during a given trip is 34%. Are making a phone call and running a red light disjoint events? Are they independent events? 10) In a group of 35 lvirginia residents, 23 Maryland residents, and 23 Delaware residents, two pecple are chosen in succession. What is the probability that the second resident will be from Delaware given that the first resident is from Maryland? 11] Six hundred people from North America [200 from each country] were randomly selected for blood type screening. with the following results: cwmwwwdwve nun\"- \"\"\"\" \"-mnm \"num \"M\" For a randomly chosen individual from this sampling of 600, what is the probability this person . . . . a} Is from Mexico? b) Has blood type A or D? o} Is from Canada and has blood type B? d) Is from USA or has blood type AB? a) Is from Mexico or has blood type B? 1"] Is from Canada. given that the person has blood type A? 9} Has blood type 0, given that the person is from Mexico? 12) Jill gets between 4 and 8 hours of sleep each night [4, 5. 6. i", or 3). She gets 4 hours 20% of the time, 5 hours 30% of the time, 6 hours 20% of the time. and she gets 7' hours twice as often as 8 hours; What is the mean and standard deviation of Jill's amount of sleep? 13) Michael invested $2000 in a certain stock. At the end of the year the stock could be worth $1600, $1350, $2200. or $2300. He thinks these changes are all equally likely, but he believes there is a 40% chance that the investment will simply stay the same. What is the mean and standard deviation of the profit on the investment? 14) A casino game has three possible winnings. $15, $10. and $5, each being twice as likely as the one before it. Player's don't win anything 65% of the time. i] What are the chances of winning $15 on one play? ii] If it costs $3 to play this game. how much does a player expect to lose on average? [Find the expected profiti which will be nggative. This is the player's loss]. 15) If two species of plants are crossbred any resulting hybrid has a 25% chance of being resistant to a certain parasite. Suppose 11 hybrids will be produced. a) Why is this situation binomial? b) What is the probability that exactly four will be resistant? c) What is the probability that at least seven will be resistant? d) What is the mean and standard deviation of the number of resistant hybrids? 16) Each moming when Mark tries to start his car. there is a 4% chance that it won't start. Assume attempts are independent. i) In the next 20 mornings. what is the probability that his car will not start at least three mornings? ii) In the next 13 mornings he attempts to start his car, what is the mean and standard deviation of the number of times his car won't start? 1?) On a particular polygraph question. it is thought that 70% of people will tell the truth. i) It 15 people are chosen at random for this polygraph trom a large population, and each is asked this question. what is the probability at most 60% of them will tell the truth? ii) It 140 people are asked this question. what is the probability that at least 75% but no more than 35% of them will tell the truth? 18) The weights of chocolate bars produced by a certain machine are normally distributed with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. 3) What proportion of chocolate bars weigh between 8.15 and 8.25 oz? b) Only 1% of these chocolate bars are below what weight? c) The middle 40% of these chocolate bars are between what two weights? 19) The number of google searches performed by US adults in one month is normally distributed with a mean of 62 and a standard deviation of 15. a) What is the probability a randomly chosen US adult has between 30 and 100 google searches in a month? b) What is the probability a randomly chosen US adult has less than 20 or more than 70 searches in a month? 6) The middle 80% of google searches per US adult in one month lies between what two values? 20) Finish times for a recent marathon had a mean of 6.1 hours and a standard deviation of 1.25 hours. The times were normally distributed. a) What proportion of runners nished in 5 hours or less? b) 10% of runners finished below what running time? c) The middle 20% of runners finished between what two times