Problem 12
In a baseball game, Tommy gets a hit \(30 \%\) of the time when facing this pitcher. Joey gets a hit \(25 \%\) of the time. They are both coming up to bat this inning. a. What is the probability that Joey or Tommy will get a hit? b. What is the probability that neither player gets a hit? c. What is the probability that they both get a hit?
Problem 13
An unfair coin has a probability of coming up heads of \(0.65 .\) The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places).
Problem 15
True/False: You are more likely to get a pattern of HTHHHTHTTH than HHHHHHHHTT when you flip a coin 10 times.
Problem 19
The following questions are from ARTIST (reproduced with permission) Five faces of a fair die are painted black, and one face is painted white. The die is rolled six times. Which of the following results is more likely? a. Black side up on five of the rolls; white side up on the other roll b. Black side up on all six rolls c. a and b are equally likely
Problem 20
The following questions are from ARTIST (reproduced with permission) One of the items on the student survey for an introductory statistics course was "Rate your intelligence on a scale of 1 to \(10 . "\) The distribution of this variable for the 100 women in the class is presented below. What is the probability of randomly selecting a woman from the class who has an intelligence rating that is LESS than seven (7)? $$ \begin{array}{|c|c|} \hline \text { Intelligence Rating } & \text { Count } \\ \hline 5 & 12 \\ \hline 6 & 24 \\ \hline 7 & 38 \\ \hline 8 & 23 \\ \hline 9 & 2 \\ \hline 10 & 1 \\ \hline \end{array} $$ a. \((12+24) / 100=.36\) b. \((12+24+38) / 100=.74\) c. \(38 / 100=.38\) d. \((23+2+1) / 100=.26\) e. None of the above.
Problem 21
The following questions are from ARTIST (reproduced with permission) You roll 2 fair six-sided dice. Which of the following outcomes is most likely to occur on the next roll? A. Getting double \(3 .\) B. Getting a 3 and a 4. C. They are equally likely. Explain your choice.
Problem 22
The following questions are from ARTIST (reproduced with permission) If Tahnee flips a coin 10 times, and records the results (Heads or Tails), which outcome below is more likely to occur, A or B? Explain your choice. $$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Throw Number } & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} & \mathbf{1 0} \\ \hline \mathbf{A} & \mathrm{H} & \mathrm{T} & \mathrm{T} & \mathrm{H} & \mathrm{T} & \mathrm{H} & \mathrm{H} & \mathrm{T} & \mathrm{T} & \mathrm{T} \\\ \hline \mathbf{B} & \mathrm{H} & \mathrm{T} & \mathrm{H} & \mathrm{T} & \mathrm{H} & \mathrm{T} & \mathrm{H} & \mathrm{T} & \mathrm{H} & \mathrm{T} \\\ \hline \end{array} $$
Problem 23
The following questions are from ARTIST (reproduced with permission) A bowl has 100 wrapped hard candies in it. 20 are yellow, 50 are red, and 30 are blue. They are well mixed up in the bowl. Jenny pulls out a handful of 10 candies, counts the number of reds, and tells her teacher. The teacher writes the number of red candies on a list. Then, Jenny puts the candies back into the bowl, and mixes them all up again. Four of Jenny's classmates, Jack, Julie, Jason, and Jerry do the same thing. They each pick ten candies, count the reds, and the teacher writes down the number of reds. Then they put the candies back and mix them up again each time. The teacher's list for the number of reds is most likely to be (please select one): a. 8,9,7,10,9 b. 3,7,5,8,5 c. 5,5,5,5,5 d. 2,4,3,4,3 e. 3,0,9,2,8
Problem 24
The following questions are from ARTIST (reproduced with permission) An insurance company writes policies for a large number of newly-licensed drivers each year. Suppose \(40 \%\) of these are low-risk drivers, \(40 \%\) are moderate risk, and \(20 \%\) are high risk. The company has no way to know which group any individual driver falls in when it writes the policies. None of the low-risk drivers will have an at-fault accident in the next year, but \(10 \%\) of the moderate-risk and \(20 \%\) of the high-risk drivers will have such an accident. If a driver has an at-fault accident in the next year, what is the probability that he or she is high-risk?
Problem 25
The following questions are from ARTIST (reproduced with permission) You are to participate in an exam for which you had no chance to study, and for that reason cannot do anything but guess for each question (all questions being of the multiple choice type, so the chance of guessing the correct answer for each question is \(1 / \mathrm{d}, \mathrm{d}\) being the number of options (distractors) per question; so in case of a 4 -choice question, your guess chance is 0.25 ). Your instructor offers you the opportunity to choose amongst the following exam formats: I. 6 questions of the 4 -choice type; you pass when 5 or more answers are correct; II. 5 questions of the 5 -choice type; you pass when 4 or more answers are correct; III. 4 questions of the 10 -choice type; you pass when 3 or more answers are correct. Rank the three exam formats according to their attractiveness. It should be clear that the format with the highest probability to pass is the most attractive format. Which would you choose and why?
