Name: ___________________________________________________ Date: ______________________
Probability & Data Analysis
EOCT Preparation
MM1D1 Students will determine the number of outcomes related to a given event.
a. Apply the addition and multiplication principles of counting
b. Calculate and use simple permutations and combinations
MM1D2. Students will use the basic laws of probabilities.
a. Find the probabilities of mutually exclusive events
b. Find probabilities of dependent events
c. Calculate conditional probabilities
d. Use expected value to predict outcomes
MM1D3. Students will relate samples to a population.
a. Compare summary statistics from one sample data distribution to another in describing center and variability of the data distributions.
b. Compare the averages of summary statistics from a large number of samples to the corresponding population parameters
c. Understand that a random sample is used to improve the chance of selecting a representative sample.
MM1D4. Students will explore variability of data by determining the mean absolute deviation (the averages of the absolute values of the deviations).
On the EOCT: 16 questions
Quiz (must pass it by Sunday at 5pm): 1st Block: http://bit.ly/math1b1st 3rd Block: http://bit.ly/math1b3rd
Computer Practice: http://www.explorelearning.com and use class code UKJN85RAFH
Study Guide: http://bit.ly/math1eoct pages 68-90
Problems
1. MM1D1 You roll a number cube 5 times. How many outcomes are possible? (For example, one outcome is 1, 2,
3, 4, 5 and another is 5, 4, 3, 2, 1)
2. You roll a number cube twice.
a. MM1D1 How many outcomes have a sum of 7?
b. MM1D2 What is the probability the sum is 7?
3. Ms. Golding offers you a pencil. She has 8 blue pencils, 7 green, 8 red, and 5 yellow.
a. MM1D2 What is the probability you get a blue pencil? (Assume you choose a random pencil)
b. MM1D2 Given that you get a blue pencil, what is the probability the person behind you gets a blue
pencil?
c. MM1D2 You and your neighbor return your pencils to Ms. Golding at the end of class. What is the
probability that 2 students from the next class also get 2 blue pencils?
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4. Hip hop star TI has agreed to perform at the 2011 prom (not really, this is just a math problem). The table
summarizes the results of a survey of every junior and senior.
a. MM1D2 Find the probability that a randomly selected junior or senior supports or has no opinion about
TI’s performance.
b. MM1D2 Find the probability that a randomly selected male opposes TI’s performance.
c. MM1D2 Find the probability that a randomly selected TI-supporter is female.
Male Female
Support
110
87
Oppose
45
96
No opinion 97
73
5. MM1D2 Ms. Golding offers you a chance to earn prizes by spinning a wheel. You pay $1 (the money goes to a
charity!) to play. The wheel has 10 sections, each with an equal probability of being selected. The prizes are
summarized in the table below. What is the expected value of playing this game?
Section of the wheel
1
2
3
4
5
Prize
Game over
Game over
Free spin again
Game over
Win $2
Section of the wheel
6
7
8
9
10
Prize
Game over
Win $5
Game over
Win $10
Game over
6. MM1D3 The heights of the members of Ms. Golding’s family are: 60”, 61”, 62”, 63”, 66”, 70”, 71”.
a. What are the mean, median, upper quartile, lower quartile, and interquartile range?
b. Ms. Brooks’ family has heights of: 64”, 65”, 66”, 66”, 67”. Who has the largest median height? And the
largest interquartile range?
7. MM1D3 Ms. Golding needs a method for getting a random sample of 5 students from her 2nd period class. Mr.
Collins needs a method for identifying 10 random ninth grade students.
8. MM1D3 The Golf Tournament histogram (below left) shows results for the first round of the Masters, held in
Augusta, Georgia over Spring Break.
a. How many people played in the golf tournament? How many players from Asia played?
b. Estimate the median score for the entire tournament and for Asian players based on the graphs.
c. Which is smaller, the median score for all players or the median score for Asian players?
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Answers
1. 66 = 46 656
2. a. 2 number cubes sum is 7 -> 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 -> 6 outcomes have a sum of 7
6
36
= probability that the sum is 7
2
7
2. b. 36 total outcomes ->
8
8
7
7
1
6
2
3. a. 8+7+8+5 = 28 = 7
3. b. 7+7+8+5 = 27
8
7
14
3. c. 8+7+8+5 ∙ 7+7+8+5 = 7 ∙ 27 = 199
4. a. Support -> 110+87=197; No opinion -> 97+73=170; Supports OR No opinion -> 197+170=367; Add all numbers
= 508; probability = 367/508 approximately 0.72
4. b. Oppose -> 45+96=141; probability = 141/508 approximately 0.28
4. c. is female / supports TI’s performance = 87/(87+110) = 87/197 approximately 0.44
5. Probability-Outcome Table:
Event
Probability Outcome
Game over 6/10
-$1
Free spin
1/10
$0
Win $2
1/10
$1
Win $5
1/10
$4
Win $10
1/10
$9
(6/10)(-$1) + (1/10)($0) + (1/10)($1) + (1/10)($4) + (1/10)($9) = $0.80
6. a. mean: 64.7”; median: 63”; upper quartile: 68”; lower quartile: 61.5”; IQR: 6.5”
6. b. median: Brooks’ family (at 66” as compared to Golding’s 63”); IQR: Golding’s family (at 6.5” as compared to
Brooks’ 1”)
7. Answers vary but all depend on all members of the population having an equal chance of being selected for the
sample.
8. a. 21+58+32+5= 116 people. 12 people from Asia.
8. b. Median is the middle score of the 116 participants. It’s the mean score of players in 58th and 59th places.
Looking at the histogram, that score must be between 71 and 75. The actual median (using the full data set,
which you don’t have) is 73. The median for Asian players is approximately 70 or maybe 71.
8. c. The median score for Asian players is smaller.
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