Unit 8 Probability and Statistics Unit Review

Ch. 9 and 10

Test

• Consists of multiple choice, true/false, and short answer all combined

• Will have a few extra credit questions built in• MUST be completed by the end of the class

period on Friday

9-7

• Independent and Dependent Events– Independent: when one event does not affect the

outcome of the other event• Ex: spinning a spinner and rolling a number cube

– Find the probability of each event as fraction and multiply them• Simplify answer

9-7

• Dependent: the outcome of the first event affects the outcome of the second event– Ex: You have a bag of marbles. You pick one

marble, DO NOT REPLACE IT, and pick another one– Number of outcomes usually changes for the second

event– Find the probability of the first event FIRST, then the

second event and multiply them• Simplify answer

9-7

There are three quarters, five dimes, and twelve pennies in a bag. Once a coin is drawn from the bag, it is not replaced. If two coins are drawn at random, find each probability. (Independent or Dependent?)

• P(a quarter and then a penny)

• P(two dimes)

9-7

The two spinners at the right are spun. Find each probability. (Independent or Dependent?)• P(less than 5 and B)

• P(odd and A)

• Using a number cube, what is the probability of rolling a 6, then a 5?

• What is the probability of flipping a coin and tails occurs four times in a row?

• A jar contains 5 blue marbles, 6 yellow marbles, and 4 green marbles. What is the probability of randomly choosing a yellow marble, not replacing it, and then choosing a blue marble?

9-1

• Probability of Simple Events• P(event) = – Probability is a number between 0 and 1• Near 0 =very unlikely• Near 1 = very likely

9-1

• Probability can be written as fraction, decimal, or percent– Simplify all fractions– Fraction to decimal• Divide numerator by denominator

– Decimal to percent• Multiply decimal by 100 (move decimal two places to

right)

• A spinner is divided into eight equal sections numbered 1-8. It is spun once. Find each probability. Write each answer as a fraction, a decimal, and a percent.

• P(not 5) P(six or less)

• P(2 or 7) P(10)

• The probability of choosing a “Go Back 1 Space” card in a board game is 25%.– If you pick a random card, what is the probability

that it is not a “Go Back 1 Space” card? Explain your reasoning.

– Write a sentence that explains how likely it is for a player in the game to random pick a “Go Back 1 Space” card.

9-2

• Theoretical and Experimental Probability– Theoretical: what should happen (what’s expected)– Experimental: what actually happens in a probability

experiment• Compare the two probabilities by changing the

fractions to decimals and writing a sentence– They are close because one fraction is close to the other

OR– They are not close because there were not enough trials

The table shows the results of a number cube being rolled 40 times.• Find the experimentalprobability of rolling a 5.• Find the theoretical probability of rolling a 5.• Compare the experimental and theoreticalprobabilities.

9-2

• Predict Future Events– Find the probability from the original problem– Simplify it– Set up a proportion with new total at the bottom

of the second fraction and solve for the missing part

• If a coin is flipped 150 times, about how many times would it be expected to land on heads?

• If a number cube is rolled 60 times, how many times would it be expected to land on a 1?

9-5

• Fundamental Counting Principle– Using multiplication instead of a tree diagram to find

the number of possible outcomes in a sample space• If there are more than 2 events, continue to multiply event

outcomes together to determine the total number of outcomes

– Show and label outcomes for each event!– If finding the probability of an event, use FCP to find the

total number of outcomes (denominator)• Usually one favorable outcome (numerator)

• Use the Fundamental Counting Principle to find the total number of outcomes for each situation.– Tossing a dime, a quarter, a penny, and rolling a

number cube– Picking a number from 1 to 30 and a letter from

the alphabet

• To drink with your dinner, you can choose water, milk, juice, or tea; with or without ice; served in a glass or a plastic cup– How many different drink combinations are

possible? If your drink is chosen at random, what is the probability of getting tea, with ice, in a plastic cup? Is it likely or unlikely that you would get this specific drink?

9-6

• Permutations– An arrangement, or listing, of objects in which order is

important– Use the Fundamental Counting Principle to find the

number of permutations– Once something is chosen, it cannot be chosen again– Use blanks for number of objects!– If finding the probability of an event, find the permutation

(total number of outcomes) first • Usually one favorable outcome (numerator)

• Martin has four books. In how many ways can he arrange them on his bookshelf?

• There are 12 students on the basketball team. In how many ways can the coach set up the starting lineup of 5 players if John will start at one of the guard positions?

• If there are 12 students on the debate team, what is the probability that Meghan will win first place, Eden will win second place, and Lorena will win third place?

10-1

• Make Predictions– Statistics: Collecting, organizing, and interpreting

data– Survey: A method of collecting information– Population: The group being studied– Sample: Part of the group that is surveyed• Must be representative of the population!

• Make Predictions Using Ratios:– Find the probability/results for the original

problem/survey and write as a simplified fraction– Set up an equivalent fraction• New number/population goes on bottom

– Solve by multiplying by same number across top and bottom or by using cross-products

– Label answer!

• A survey found that 17 out of 20 teens eat breakfast every morning. What is a reasonable prediction for the number of teens out of 1,280 in a school who eat breakfast every morning?

• A survey showed that 70% of students would select roller coasters as their favorite ride at an amusement park. Out of 5,000 students, predict how many would NOT select roller coasters as their favorite ride.

The table shows the results of a survey at Scobey Middle School about students’ favorite cookies. • There are 424 studentsat Scobey Middle School. About how many can be expected to prefer chocolatechip cookies?

10-2

• Unbiased and Biased Samples– Unbiased = GOOD! (Valid results)

• Accurately represents the entire population• Simple Random Sample• Systematic Random Sample

– Biased = BAD! (Not valid results)• One or more parts of the population are favored over others• Convenience Sample• Voluntary Response Sample

• Antwan wants to know how often the residents in his neighborhood go to the beach. Which sampling method will give valid results?– A. He asks all the members of the swim team at his

school– B. He asks all his family members and friends– C. He posts a question on a community Web site– D. He asks three random households from each street

in his neighborhood

• Determine whether the conclusion is valid. Justify your answer.

• To determine the most common injury cared for in an emergency room, a reporter goes to the same hospital every afternoon for one month during the summer and observes people entering the emergency room. She concludes that second degree sunburn is the most common injury.

• To evaluate the defect rate of its memory chips, an integrated circuit manufacturer tests every 100th chip off the production line. Out of 100 chips tested, one chip is found to be defective. The manufacturer concludes that 3 chips out of 300 will be defective.

MMMR

• Mean: average of a data set– Add the numbers and divide by how many there are

• Median: middle of a data set– Put the numbers in order and cross out number on both

ends until you find the number in the middle• If even amount of numbers, find the average of the middle two

• Mode: number(s) that occur the most often• Range: spread of the data– Subtract the lowest number from the highest

• The number of toys donated by students in 12 classes is shown below. Find the mean, median, mode, and range of the data.

24, 33, 59, 19, 16, 29, 20, 17, 31, 23, 16, 25

10-5

• Select an Appropriate Display– Bar Graph: show the number of items in specific categories– Box Plot: show measures of variation (median) for a set of

data– Circle Graph: compare parts of the data to the whole

(percents)– Double Bar Graph: compare two sets of categorical data– Histogram: show frequency of data divided into equal intervals– Line Graph: show change over a period of time– Line Plot: show frequency of data with a number line

Select an appropriate display for each situation. Justify your reasoning.

• ages of all students at a summer camp

• test grades for a class, arranged in intervals

10-4

• Compare Populations– Median: breaks data in half– First Quartile: median of first half of data– Third Quartile: median of second half of data– Interquartile Range: Third quartile – first quartile

• You can draw inferences about two populations in a double box plot or double dot plot by comparing their centers and variations– If both sets of data are symmetric:

• Use mean

– If neither set of data is symmetric or one set of data is symmetric:• Use median for measure of center AND• Use interquartile range for measure of variation (spread of

the data)

• The double line plot shows the number of hours each month 2 groups of students reported that they watched TV.

Which of the following statements is true?

• A. Group 1 has a greater median number of hours that they watched television. Group 1 has a smaller interquartile range, so the data is less spread out.

• B. The mean for group 2 is larger than the mean for group 1.• C. The median for group 2 is larger than the median for group 1.• D. Both sets of data are symmetric. You should use the mean to

compare the measures of center and the mean absolute deviation to compare the variations

The double line plot shows the number of students who attended the home games of the baseball team for two recent seasons.

Which of the following statements is not true?• A. The attendance for 2009 was more varied.• B. The attendance for 2010 was more

consistent.• C. The attendance for 2009 peaked at 23

students.• D. The attendance for 2010 ranged from 20 to

27.

Compare the centers and variations of the two populations. Round to the nearest tenth if necessary. Write an inference you can draw about the two populations• The double plot shows the daily attendance for two fitness

clubs for one month