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AP Statistics – Chapter 6 – Simulations & Probability – Study Guide

10 / 30 / 10 / 30 / 10
20 / 10 / 50 / 10 / 20
  1. A new clothing store advertises that during its Grand Opening every customer that enter the store can throw a bouncy rubber cube onto a table that has squares labeled with discount amounts. The table is divided into ten regions. Five regions award a 10% discount, two regions award a 20% discount, two regions award a 30% discount, and the reaming region awards a 50% discount. Show your work.
  2. What is the probability that a customer gets more than a 20% discount?
  3. What is the probability that a customer gets less than a 20% discount?
  4. What is the probability that the first two customers both get a 50% discount?
  5. What is the probability that none of the first three customers gets more than a 30% discount?
  6. What is the prob. that the 1st customer to win a 30% discount is the 6th customer that enters the store?
  7. What is the probability that there is at least one customer to win a 50% discount among the first five customers that enter the store?
  8. As you enter the store you watch the four people in front of you all win 50% discounts. The store manager tells you how lucky you are to be throwing the cube, while it is on a hot streak, but the friend with you says you’re unlucky because the streak can’t continue. Comment on their statements.
  1. A survey of families revealed that 58% of all families eat turkey at holiday meals, 44% eat ham, and 16% have both turkey and ham to eat at holiday meals.
  2. Create Venn Diagram for this given scenario.
  3. What is the prob. that a family selected at random had neither turkey nor ham at their holiday meal?
  4. What is the probability that a family selected at random had only ham without having turkey at their holiday meal?
  5. What is the probability that a randomly selected family having turkey and ham at their holiday meal?
  6. Are having turkey and having ham disjoint events? Explain.
  1. Many school administrators watch enrollment numbers for answers to questions parents ask. Some parents wondered if preferring a particular science course is related to the student’s preference in foreign language. Students were surveyed to establish their preference in science and foreign language courses.
  2. What is the probability that you are taking Biology and Spanish?
  3. What is the probability if you are taking French, that you are also taking Physics?
  4. What is the probability that if you are taking Chemistry, that you are also taking French?
  5. Does it appear that preferences in science and foreign language are independent? Explain.

Chemistry / Physics / Biology / Total
French / 16 / 10 / 8 / 34
Spanish / 35 / 23 / 44 / 102
Total / 51 / 33 / 52 / 136
  1. For purposes of making budget plans for staffing, a college reviewed student’s year in school and area of study. Of the students, 22.5% are seniors, 25% are juniors, 25% are sophomores, and the rest are freshmen. Also, 40% of the seniors major in the area of humanities, as did 39% of the juniors, 40% of the sophomores, and 36% of the freshmen. Show your work.
  2. Make a tree diagram for the scenario. List the probabilities on each branch.
  3. What is the probability that a randomly selected humanities major is a junior?
  1. Given that A and B are independent events and P(A) = .4, P(B) = .5, find the values of

Blood Type / O / A / B / AB
U.S. probability / 0.45 / 0.4 / 0.11 / ?
  1. All human blood can be “ABO-typed” as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in the United States.
  2. What is the probability of type AB blood in the United States?
  3. An individual with type B blood can safely receive transfusions only from persons with type B or type O blood. What is the prob. that the husband of woman with type B blood is acceptable blood donor for her?
  4. What is the prob. that in a randomly chosen couple the wife has type B blood and the husband has type A?
  5. What is the prob. that one of a randomly chosen couple has type A blood and the other has type B?
  6. What is the probability that at least one of a randomly chosen couple has type O blood?
  1. Use simulation to find the demand for cheesecake on 30 consecutive business days (Find the average number of cheesecakes sold over a 30 period day.). The owner of a bakery knows that they daily demand for a highly perishable cheesecake is as follows:

Number/Day / 0 / 1 / 2 / 3 / 4 / 5
Relative Frequency / 0.05 / 0.2 / 0.25 / 0 / 0.2 / 0.1
  1. On January 1 of every year, many people watch the Rose Parade on television. The week before the parade is very busy for float builders and decorators. Roses, carnations, and other flowers are purchased from around the world to decorate the floats. Based on pat experience, on e float decorator found that 10% of the bundles of roses delivered will no to pen in time for the parade, 20% of the bundles of roses delivered will have bugs on them and be unusable, 60% of the bundles of roses will turn out to be beautiful, and the rest of the bundles of roses delivered will bloom too early and start to discolor before January 1. Conduct a simulation to estimate how many roses the float decorator will need to purchase to have 15 good bundles of roses to place on the float.
  2. Describe how you will use a random number table to conduct this simulation
  3. Show three trials by clearly labeling the random number table given below. Specify the outcome for each trail.
  4. State your conclusion.

37542 / 4805 / 64894 / 74296 / 24805 / 24037 / 20636 / 10402 / 10822
18422 / 68953 / 19645 / 9303 / 23209 / 2560 / 15953 / 34764 / 35080
99019 / 2529 / 9376 / 70715 / 38311 / 31165 / 88675 / 74397 / 4436
12807 / 99970 / 80157 / 36147 / 64032 / 36653 / 98951 / 16877 / 12171
  1. Independence of events is not always obvious. Toss two balanced coins independently. The four possible combinations of heads and tails in order each have probability 0.25. Determine if the events A = “head on first toss” and B = “both tosses have the same outcome” are dependent or independent.
  1. The genes that determine the eye color – red and white – of fruit flies are (R,W). The offspring receive one eye-color gene from each parent. (a) Define the sample space for the eye-color genes of the fruit fly offspring, assuming that each of the four possible outcomes is equally likely. (b) If a fruit fly offspring ends up with either two red genes or one red and one white gene, its eyes will look red. Given that an offspring’s eyes look red, what’s the conditional probability that it has two red genes for eye color?
  1. Study your notes!! You need to know vocabulary and what the major concepts are. Read over pages 457-458.