Stats
Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that girls will place 1st, 2nd, and 3rd in the marathon?
1/114
Annie writes the numbers 1 through 10 on note cards. She flips the cards over so she cannot see the number and selects three cards from the stack. What is the probability that she has selected the cards numbered 1, 2, and 3?
1/120 For this problem, the probability for drawing 1, 2, or 3 for the first card is 3/10, second card is 2/9, and the third card is 1/8. Multiply these together and you get 6/720 or 1/120.
Jane has cards with the letters ALABAMA on them. She lays the cards face down. What is the probability of Jane selecting two cards and both of them being a vowel?
2/7 here n = number of letters = 7 r = number of selection = 2 Number of possible outcome 7C2 = 7! /2!(7-2)! = 21 possibilities Now, the number of favorable outcomes n = number of vowels : 4 (we have 4 times A) r = only 2 vowels required, number of favorable outcomes = 4C2 = 4!/2!(4-2)! = 6 Required probability = 6/ 21 = 2/7
In a fish tank there are 10 clown fish, 4 angel fish, 6 puffer fish, and 5 eels. What is the probability of scooping out a clown fish on the second scoop after scooping out a clown fish on the first scoop and not replacing it?
3/8
A class of 6 boys and 12 girls are preparing for finals. The teacher is going to select 3 students to be exempt from the test. What is the probability that the three students that are exempt will be all boys?
5/204 n, is the number of item, and in this case total number of boys and girls = 6+12=18 r, is the number of item being chosen at a time, r = 3 Number of outcomes = 18C3 = 18!/3!(18-3)! =816 Now since there are 6 boys and selection is for 3, n term would be 6 and r term would be 3. Our equation would be 6C3 = 6!/3!(6-3)! = 20 Required probability = 20/816 = 5/204
What is the mode of this data set of the number of baby rabbits born to different mother rabbits? {6, 4, 5, 8, 6, 7, 8, 2}
6 and 8
Jonathan knows he scored in the 25th percentile on his psychology test. The professor gives the students the following list of grades (without names): 51, 37, 87, 95, 99, 78, 63, 96, 68, 84, 92 Assuming that there are 11 students in the class, what was Jonathan's test score?
63
Twelve employees at a local company decide to go out for lunch. Of the 12 employees, 8 are men and 4 are women. If a woman is the first to order, what is the probability that a man will be the next person to order lunch?
8/11
Theoretical Probability
Probability based on comparing the number of possible favorable outcomes to the number of total possible outcomes
Factorial
The product of all whole numbers except zero that are less than or equal to a number ex: 4! = 4 x 3 x 2 x 1
A student makes a dot plot to represent the grades their classmates got on the last test, and finds that it makes a shape that is mirrored nearly perfectly across a line at the mean. Is this shape symmetrical? Why or why not?
Yes, it's symmetrical, because the shape is mirrored nearly perfectly across a line.
frequency distribution
a list of how often each value occurs
What is a histogram also known as?
bar graph
Which of the following is least likely to be reported due to it being the one most likely to change by the introduction of additional scores? mean median or mode?
mode Mode is the most often occurring number. This is likely never going to be reported unless you're looking at a very specific piece of literature.
Given rank and population, which formula do you use to find the percentile?
( k + .5r) / n = p k= numbers at or below the given rank r= numbers equal to the rank n= total number of teams p= percentile
In Mr. Martin's math class there are 15 students out of which 4 will be selected to receive a special award. How many combinations of students can be selected?
1,365 n = number of students = 15 r is the number of items being chosen at a time = 4 Number of combination = 15C4 = 15!/4!(15-4!)=1365
To find Hollys grade I will
1- multiply the number of students (15) by the percentile (.90) to find the index 15x.90= 13.5 2- round 13.5 up to 14 3- Then I will write the scores in ascending order and count up to 14 in the set 4- Her score was a 94
A locker combination contains four numbers between 1 and 20 and none of the numbers can be repeated. What is the probability that the locker combination will consist of all even numbers?
14/323 This problem involves finding two permutations: the number of total possible combinations and the number of possible combinations with only even numbers. The final probability is (even # combos/all possible combos), which reduces to the correct answer. The probabilities for the even numbers are 10/20, 9/19, 8/18, and 7/17. When you multiply these together and reduce the product you get 14/323.
A bag has been filled with 35 red marbles, 25 green marbles, 25 blue marbles and 15 orange marbles. What is the theoretical probability that someone can reach in and randomly pick an orange marble?
15 out of 100, which is 15/100 (15%)
What is the mean of this data set: 4, 5, 6, 7, 4, 5, 8?
5.57
The probability of winning a prize at a ball toss at a carnival is 2/7. What is the probability of not winning a prize?
5/7
Phyllis is also in Jonathan's psychology class. She knows she scored in the 90th percentile on his psychology test. The professor gives the students the following list of grades (without names): 51, 37, 87, 95, 99, 78, 63, 96, 68, 84, 92 Assuming that there are 11 students in the class, what was Phyllis's test score?
96
All of the students in Jasmine's class have had their height measured. Jasmine is the 12th tallest person out of 560 students. What percentile is Jasmine's height in?
98th
What is an element?
A collection of anything: numbers letter
What is a set?
A collection of elements
Histogram
A graph of vertical bars representing the frequency distribution of a set of data. looks like a bar graph
Kim has two dice. She needs to both to land on 6 to win the game. What is the probability of kim rolling two 6's in a row?
First dice = 1/6 chance second dice= 1/6 chance 1/6 X 1/6 = 1/36 chance
What is a subset?`
If every element in one set is included in another set, the first is a subset of the second
What can we show using a histogram?
The mode of the data set.
A permutation is Formula
a method to calculate the number of events occurring where order matters nPr = n! / (n - r)!
conditional probability
a type of dependent event involves finding the probability of an event occurring based on a previous event already taking place
Combinations
a way to calculate the total outcomes of an event where order of the outcomes does not matter
A dot plot is a visual representation of data using intervals or categories of variables, with each dot representing _____.
an observation in the data
Dependent events
events in which the previous attempts affect the outcome of subsequent events. An example of a dependent event would be selecting a card from a deck of cards and not replacing the card. Then you draw another card from the now-smaller deck of cards.
probability
likelihood that a particular event will occur
Intersection
n elements in K AND T
Combination Formula
nCr = n!/r!(n-r)! n= total number of items r= number of items being chosen at a time
What is the shape of a graph that peaks to the left or the right of the center?
skewed
Complement
when a set is subtracted or not included in the set K'= everything not in the kitchen
Union
when two or more sets are united Elements in K or T
Intersection between sets
when two or more sets intersect, or are common objects, in sets
What is the term for data that is grouped by type or object, not by numbers?
categorical
What is the term for the type of data that is measurable?
numerical
The probability of simple events is Formula
the probability of a single event occurring # of favorable outcomes/Total # of outcomes Answer must be in simplest form!
The formula for compound events is
the same as simple events: number out favorable outcome/total number of outcomes However, once you get the probability of both events, you multiply them together
Using a standard deck of 52 cards, what is the probability of selecting a 4 and then after not replacing the card, selecting another 4?
1/221
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and and 3 jazz CDs. What is the probability that the first CD that Kyle pulls from the box will NOT be hip hop?
3/5 There are 18 CDs that are NOT hip hop out of the 30 total CDs. The ratio is 18/30 which reduces to 3/5.
Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that boys will place 1st, 2nd, and 3rd in the marathon?
91/228 To solve this problem, must look at the probabilities the the top three runners are boys and multiply them together, 15/20 x 14/19 x 13/18 = 91/228.
At a local ice cream parlor, there are 6 different flavors of ice cream from which to select (strawberry, chocolate, vanilla, rocky road, mint chocolate chip, and peanut butter). Each ice cream sundae must include 2 different flavors of ice cream; what is the probability that the next customer's sundae will have vanilla and chocolate?
1/15 n = no of different flavors =6 r = number of flavor to be selected = 2 Possible outcomes = 6C2 = 6!/2!(6-2)! = 15 Now let us calculate the number of favorable outcomes n = vanilla and chocolate = 2 r = 2 Favorable outcome = 2C2 = 1 Required probability = 1/15
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and and 3 jazz CDs. What is the probability that Kyle will select a jazz CD from the box, and then, without replacing the CD, select a country CD?
1/29 Probability of getting a jazz CD 3/30 or 1/10. Probability of getting a country CD after selecting a jazz CD and not replacing it is 10/29. 1/10 x 10/29 = 10/290 = 1/29
If stacy scored in the 90th percentile, that means she scored
at or above 90% of her class
What does these mean in sets: E _C_ (underlined) U n
element subset union intersection
Complementary events
events that add together to equal a whole or one ex: if the probability of it raining today is 2/5, then the probability of it not raining is 3/5
Independent events
events that do not affect the outcome of subsequent events. In an independent event, each situation is separate from previous event An example of an independent event would be selecting a card from a deck of cards and then returning the card to the deck. After you return the card, select another card from the same, equal deck
Which axis of a histogram usually shows the categories into which the various members of a data set fall?
horizontal
Disjoint set
sets that have no elements in common with any other set other than the universal set
Jenny has a bowl of M&M's that has 6 brown, 3 green, 4 red, and 12 yellow M&M's. She selects a yellow M&M and does not replace it. What is the probability that her second selection will be a brown M&M?
1/4
Kate and Kyle are playing a game. They must flip a coin and spin a spinner that has 12 equal sections numbered 1 through 12. What is the probability that Kyle will flip a heads and spin the spinner and get an even number?
1/4
A newspaper company is selecting four houses to receive a free newspaper on your block. There are 10 houses on your block that are numbered 1-10. What is the probability that the four houses selected for a free newspaper will all be even numbered houses?
1/42 r is the number of items being chosen at a time = 4, that is r = 4 10C4 = 10!/4!(10-4)! = 210 is the number of possible outcomes. Number of favorable outcome (even number) = 5 Required probability = 5/210 = 1/42
All of the letters of MISSISSIPPI are put in a bag. What is the probability of selecting an M and then after not replacing the letter, selecting a P?
1/55
If you roll a die three times, what is the probability of rolling only even numbers?
1/8
The letters that spell out the state CALIFORNIA are cut and placed in a bag. What is the probability that the 3rd letter selected will be a C if the first two letters selected were both I's? (Letters were not replaced)
1/8
Using a standard deck of cards (which has 26 red cards and 26 black cards, with 13 cards of every suit), what is the probability of selecting a red card, and then after replacing the card, selecting a heart card?
1/8
While playing with a standard deck of playing cards, what is the probability that Jim's 5th card will be red after selecting 4 cards that were also red and not replacing them? (Hint: There are 52 cards in a deck which contains 26 red and 26 black cards.)
11/24
What is the median in this data set for the number of cupcakes eaten per person at a cupcake eating contest? {10, 20, 15, 10, 30, 21, 18, 12}
16.5
All of the letters that spell MISSISSIPPI are put into a bag. What is the probability of selecting a vowel, and then after replacing the letter, also drawing an S?
16/121
Susanne has a set of data she is using to create a histogram. If the set of numbers below is her data set, then which number in the data set will create the highest peak? 2,2,3,5,6,7,8,6,5,2,3,4,2,5,6,2
2
Holly's professor posts a list of grades, without the names, on the blackboard. There are 15 students in the class and 15 grades on the board. The grades are: 85, 34, 42, 51, 84, 86, 78, 85, 87, 69, 94, 74, 65, 56, 97. To find Holly's grade, we need to do the following steps:
Multiply the total number of values in the data set by the percentile, which will give you the index. Order all of the values in the data set in ascending order (least to greatest). If the index is a whole number, count the values in the data set from least to greatest until you reach the index, then take the index and the next greatest number and find the average. If the index is not a whole number, round the number up, then count the values in the data set from least to greatest, until you reach the index.
Dave has a fantasy football league with his coworkers. Dave's team is ranked third out of 35 teams in his office. In what percentile is Dave's team?
Use ( k + .5r) / n = p k: 35-3= 32 r: 1 (only person in 3rd place) n: 35 teams (32 + .5(1)) / 35 = P 32.5/35= 92.8% round up = 93rd percentile
Compound events involve
the probability of more than one event happening together
Jimmy has the letters for the state of MISSISSIPPI written on cards, one letter per card. He turns the cards over and mixes up the order. If he selects one card at a time without replacing the cards, what is the probability that he will spell the word MISS in order?
To calculate the probability, we need to know the total outcomes and the favorable outcomes. The total outcomes would be 11 x 10 x 9 x 8 because he only needs to select 4 cards and there were 11 cards and they are not being replaced. This equals 7,920. Favorable outcomes would be 1 x 4 x 4 x 3. For the first blank, there is only one M so a 1 goes in the first blank. The second blank, there are 4 I's, so a 4 goes in the 2nd blank. The 3rd blank, there are 4 S's and the 4th blank there are only 3 S's because one was already selected. This would equal 48. Probability equals favorable outcomes over total outcomes. So, 48/7,920 equals 1/165.
Data set
a collection of numbers or values that relate to a particular subject. For example, the test scores of each student in a particular class is a data set. The number of fish eaten by each dolphin at an aquarium is a data set
percentile
a measure that indicates what percent of the given population scored at or below the measure.
