cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 1Exam III Review ProblemsFall 2011Note: Not every topic is covered in this review.Please also take a look at the previous Week-in-Reviews for more practice problems.1. Determine whether the following statements are Tr ue or False.(a) The number of minutes it takes you to us e an ATM machine is an infinite discrete random variable.(b) An experiment consists of drawing cards, without replacement, from a standard 52-card deck until all4 Aces have been drawn. Let X represent the number of draw s needed.X can be any value in the set {1, 2, 3, . . . , 52}.(c) The number of cadets in a class of 100 students is a finite discrete r an dom variable.(d) T he odds of drawing an Ace from a standard 52-card deck on the second draw, if cards are drawnwithout replacement and it is known that the first card draw n was a king, are 4 to 47.(e) If the odds against an event E occurring are 3 to 19, then P (E) =1922.(f) The total area of a probability histogram is equal to 1.(g) An experiment with n outcomes will have 2nsimple events.cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 22. There are 130 boxes of Cheerios in a grocery store. The following table tells you how many boxes had acertain nu mber of Cheerios in them.# of C heerios510 480 467 434 521 555# of Boxes 23 17 40 30 9 11(a) Place an X in the row of the table which represents the variable being measured.(b) Find the mean, median, mode, standard deviation, and variance for X.(c) Find the pr ob ab ility distribution of X.(d) Find P (X ≥ 500).cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 33. Suppose you pay $10 to roll two fair six-sided dice and sum the numbers that show. You win twice whatyou paid if a 7 or 11 show s up. You lose what you paid if a 2,3, or 12 shows up. For anything else thatshows up, you win $5. Let X be your net winnings.(a) What are your expected net winnings?(b) How much should be charged to make this a fair game?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 44. Determine whether or not the following experiments are binomial.(a) Roll a pair of fair six-sided dice 10 times and observe whether or not a sum of 2 is rolled.(b) Roll a fair six-sided die 8 times and note the number rolled.(c) Toss a fair coin until a head is tossed.(d) Pick 4 marbles, in s uccession without replacement, from a box with 4 red and 5 green marbles andobserve the color of the marble picked.(e) Pick a marble from Box 1 containing 4 red and 5 green marbles and observe the color of the marblepicked. Pick a marble from Box 2 containing 3 red and 6 green marbles and observe the color of themarble picked.5. 15% of a given population is left-handed. A sample of 50 people from the population is selected at random.What is the probability that(a) Exactly 8 people are left-handed?(b) At most 15 people are left-handed?(c) More than 11 people are left-handed?(d) Between 6 and 20 people are left-hand ed?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 56. You roll a weighted six-sided die 500 times.The die is weighted such that the prob ab ility of the die showing a 1 is 0.8.(a) What’s the probability that exactly 408 ones are rolled?(b) What’s the probability that at least 375 ones are rolled?(c) What’s the probability that fewer than 390 ones are rolled?(d) How many ones should you expect to roll?(e) What is the variance and standard deviation in the number of ones rolled?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 67. The table below gives the results of a survey conducted at Idea University regarding wh ether or not studentsenjoy studying math and/or history. Use the information to answer the questions which follow.Enjoy Only Math Enjoy Only History Enjoy Math and History Enjoy Neither Total(T) (H) (B) (N)Females (F) 35 20 15 10 80Males (M) 40 45 25 5 115Total 75 65 40 15 195(a) What is the probability that one of the surveyed s tudents picked at random is a male who enjoys onlyhistory?(b) What is the probability that one of the surveyed students picked at random enjoys history or math?(c) If a male is selected at random, what is the probability th at he enjoys studying history?(d) What is the probability that a randomly selected female does not enj oy studying either subject?(e) What is the probability that a randomly seleted student who enjoys studying math also enjoys studyinghistory?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 78. You have a uniform sample space S = {s1, s2, . . . , s6} for an experiment with eventsA = {s1, s2, s3, s4} and B = {s2, s4, s6}.(a) Draw a probability distribution for this experiment.(b) Compute P (A ∩ B)(c) Compute P (A ∪ B)(d) Compute P (A|BC)(e) Are A and B independent events? Why or why not? (Use correct mathematical justification.)cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 89. Let E and F be two events with P (E) = 0.35, P (F ) = 0.55, and P (E ∩ FC) = 0.15.Answer the following questions.(a) P (E ∩ F ) =(b) P (E|F ) =(c) P (E ∪ F ) =(d) Compute the prob ab ility of exactly one of these events (E or F ) occurring.(e) Are E and F mutually exclusive? Why or why not?(f) Are E and F independent? Why or why not?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 910. A box contains 21 candles: 10 white, 3 red, 6 green, and 2 navy. You lose electricity and rand omly select 6candles from the box to use for light. What’s the probability th at you select(a) Exactly 3 white candles?(b) At least 2 green candles?(c) Exactly 2 red or exactly 3 green candles?cKathryn Bollinger and Benjamin Aurispa, November 10, 2011 1011. A math class has a row of 14 students with 8 freshmen, 2 juniors, an d 4 seniors. What is the probabilitythat they are seated with all students of the same classification sitting next to one another?12. Use the partially drawn tree to the right to compute the following probabilities.(a) P (C|B)(b) P (B ∩ C)(c) P (B|C)(d) P (CC)0.700.250.200.150.60ABDEDECCcKathryn Bollinger and Benjamin Aurispa, November 10, 2011 1113. A chef’s school is 60% male. Seventy percent of the males and 90% of th e females like eating beef Wellingtonfor dinner. A student of the school is selected at random.(a) Draw a tree diagram r epresenting this situation.(b) What is the probability that the student is male or likes eating beef Wellington for d inner?(c) If the student likes eating beef Wellington for dinner, what is the
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