cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 1Week-In-Review #7 (7.2, 7.3, 7.4)1. A pair of fair 6-sided dice are rolled and the outcomes on each die are recorded.(a) Write an appropriate sample space for this experiment.(b) Is this a uniform sample space? Why or why not?(c) How many simple events are associated with this experiment?(d) How many total events are associated with this experiment?(e) Write the event, E, that a sum of less than 6 is rolled.(f) Find P (E).(g) Find the probability that a produ ct of 8 is rolled or a 5 is rolled on at least one of the dice.(h) Find the probability that a sum of 8 is rolled or a double is rolled.(i) Find the p robability that a sum of 2 and at least one 3 is rolled.cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 22. You roll two fair five-sided dice (one red and one green). What is the probability that the(a) Sum of the dice is 7?(b) Red die shows a bigger number th an the green die?(c) Sum of the dice is odd and the green d ie shows a 2?(d) Red die shows a 2 or the green die shows a 4?(e) Number 3 is not r olled on either die?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 33. You choose one letter at random from the word HALLOWEE N.(a) Write a uniform sample space for this experiment and the correspondingprobability distribution.(b) Write a non-unif orm sample space for this experiment and the correspondingprobability distribution.4. A chick is randomly chosen from a new box of multi-colored Peeps containing 3 yellow, 4 purple,2 green, 1 red, and 6 pink chicks an d its color is noted.(a) Write a non-uniform probability distribution for this experiment.(b) What is the probability that a green or red chick is chosen?(c) What is the probability that a traditional yellow ch ick is not chosen?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 45. Suppose P (E) = 0.4, P (F ) = 0.5, and P (E ∪ F ) = 0.6. Calculate the following.(a) P (E ∩ F )(b) P (FC)(c) P (EC∪ FC)(d) P (E ∩ FC)cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 56. For Sunday dinner, the Smith family and the Jones family go out to eat. Twenty percent ofthe time the Smiths go to th e Elite Diner. Thirty percent of the time the Joneses go to the E liteDiner. Twelve percent of the time both families go to the Elite Diner.What is the pr ob ab ility that on any given Sunday,(a) At least one of the families goes to the Elite Diner?(b) Exactly one of the families goes to the Elite Diner?(c) Neither of the two families goes to the Elite Diner?7. 300 students were recently surveyed. 200 of these students were taking MATH 141, 95 said theyregularly use their cell phone in all of their classes, and 80 are not taking MATH 141 and alsodo not regularly use their cell phone during any of their classes. What is the probability that arandomly selected surveyed student(a) Regularly uses th eir cell phone in their MAT H 141 class?(b) Does not regularly use their cell phone during their classes?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 68. The stud ents in a statistics class were surveyed concerning their eye color. The findings wer egathered in the table below.Blue Eyes (B) Green Eyes (G) Brown E yes (W ) Other (O) TotalsFemales (F ) 15 8 25 3 51Males (M ) 10 5 12 7 34Totals 25 13 37 10 85For each question below, write the corresponding probability notation for the question being askedand then find the nu merical answer.What is the pr ob ab ility that a randomly selected surveyed statistics student(a) Is female?(b) Has blue eyes?(c) Is female and has blue eyes?(d) Is female or has blue eyes?(e) Does not have green eyes?(f) Is a male or does not have brown eyes?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 79. A survey of 5902 adults revealed the following:Has s een ghost Has not seen ghost TotalAge 18-29 212 1313 1525Age 30 or over 465 3912 4377Total 677 5225 5902Let Y = adult is un der 30, V = adult is 30 or over ,G = adu lt has seen a ghost, N = adult has not seen a ghostFor each question below, write the corresponding probability notation for the question being askedand then find the nu merical answer.(a) What is the probability that a randomly selected adult has reportedly seen a ghost?(b) What is the probability that a randomly selected adult is under 30 and h as seen a gh ost?(c) What is the probability that a randomly selected adult is under 30 or has seen a ghost?10. A bag contains 4 red disks, 7 green disks and 8 blue disks. Suppose a sample of 6 disks areselected at r an dom. What is the probability that the sample contains(a) Exactly 3 red and 3 blue disks?(b) Exactly 5 green disks?(c) All the available red disks ?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 8(d) At least 2 blue disks?(e) No more than 1 green disk?(f) All disk s of the same color?(g) Exactly 2 green or exactly 3 blue disks?cKathryn Bollinger and Benjamin Aurispa, October 28, 2011 911. In order to use an ATM m achine, you must have a 4-digit pin number. Suppose that to pickyour pin , you number pieces of paper from 0 through 9 and place them in a bag. You then draw4 pieces of paper from the bag, in succession, with replacement. The first number d rawn becomesthe first digit of you r pin the second number drawn becomes the second digit, etc. What is theprobability that your pin number will have exactly three 2’s in it?12. You roll a fair six-sided d ie 10 times. Each time a 5 is rolled you receive $5. What’s theprobability that you receive at least
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