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# Math Hope

### Math Sections

Experimental Probablity is probablility based on data collected from repeated trials
A toy car manufactor inspected 2000 toy cars at random. The manufactor found no defects in 1899 toy cars. What is the probablity that a car selected at random had no defects? Write the probability as a percent. Experimental Probablitity: 1899/2000= 0.9495= 94.95= 95%
Theoretical Probability P(event= number of favorable outcomes/number of possible outcomes
Suppose a bag contains 2 black, 3 blue, 3 green and 2 red marbles. 1-What is the probability of reaching into the bag randomely selecting a red marble? 2-What is the probability of randomly selecting a red or black marble? Theroretical Probability: 1- 2/10=1/5 (1.0/5=.2= 20%) 2- 4/10=2/5=.4= 40%
Geometric Probability Desired outcome/Total outcome
You purchase 1 raffet ticket. 500 are sold. What is the probablitites? P (Win) = 1/500, P (loss)= 499/500
Tickets sold by class: 9th grade 500 blue tickets 10th grade 650 red tickets 11th grade 700 green tickets What is the probability that the winning ticket was sold by an 11th grader? P= 700/ (500+650+700)= 700/1850
Mutually Exclusive Events can't occur at the same time
If A+B are mutually exclusive events then... P(A or B)=P (A)+P(B)
If A+B are not mutually exclusive events then... P(A or B)= P(A)+P(B)-P(A and B)
24% of the students at the local high school are seniors, 16% are juniors, 34% are sophomores and 26% are freshmen. If a student is chosen at random from school, what is the probability the student is a senior or a junior? Mutually Exclusive P(senior or junior)= P(senior) + P (Junior) = .24 + .16 = .40 = 40%
There are 5 types of fish in the tank at the pet store. 10% of the fish are tiger-striped, 20% are angelfish, 15% are catfish, 30% are tetras, & 25% are zebra fish. What is the probability that Joe gets a zebra fish or a tiger-striped fish? Mutually Exclusive P(zebra or tiger)= P(zebra)+P(tiger) = .25 + .10 = .35 = 35 %
Dependent Events Affect each other P(A then B)=P(A) P(B after A)
A bag contains 6 red and 4 blue marbles. What is the probability of randomly selecting a red, then a blue marble, without replacing the first? Dependent Event P(red)=6/10 =3/5 P(blue after red)=4/9 P(A) x P(B after A) 3/5 x 4/9= 12/45 = 4/15
Independent Events Dont influence each other
Suppose the letter tiles shown were despoited in a bag. What is the probability of randomly selecting an I and a U? Independent Event P(I)=2/15 P(U)=2/15 P(I+U)= 2/15 x 2/15= 4/225
Tree Diagram Suppose you go to a deli which has 3 types of bread, 3 types of meat for possible sandwich combinations. How many combinations can you make? (Answer 9)
Counting Principle When tree diagram is to big (M x N)
At the weeding there are 5 salad choices, followed by 6 choices for the main course. How many ways can you choose a salad folloed by a main course? Counting Principle (5 x 6=30 choices)
Chandy throws an even fancier wedding and serves a 5 course meal. There are 3 choices for each course. How many different meals can be chosen? 1 2 3 4 5 = courses 3 x 3 x 3 x 3 x 3 = 243 meals
Find the number of permutations possible for the letters NESTA. N E S T A 5 x 4 x 3 x 2 x 1= 120
Sam, Janet, and Bob wait in line for a concert. In how many wasy could the 3 of thme line up? 3 x 2 x 1=6
Permutations nPr= n (n-1)(n-2)... Order Matters!!!
Simplify 8P5 n=8, r=5 8(8-1)(8-2)(8-3)(8-4) 8 x 7 x 6 x 5 x 4 6720
Combinations Order doesn't matter!!
Combinations nCr= n! ______ r!(n-r)!
A 3 person committe is to be chosen from a group of 15 students. In how many ways can the students be chosen? 15C3 Answer... 455
nCr Stand for the number of cominations of n objects chosen r at a time
nCr nPr --- rPr
There are 7 pizza toppins, you can choose 3. n=7 r=3 7C3=7P3=7 x 6 x 5= 210 --- --------- 3P3 3 x 2 x 1 =6 = 35
Mean add them all up and divide by #
Mode # that accures the most
Median Middle #
IQR Q3(median) - Q1(median)
Variance All the numbers individually subtract the mean, then squared. Total them then divided by the additives
Standard Deviance Variance square root
Solving cryptarithm Guess and check
The sum of two consecutive terms in arithmetic sequence 2,7, 12, 17... 499. Find the 2 terms. n=the first n+5= second term n + n + 5= 499 2n + 5 =499 2n = 494 n=247, n+5=252
Communtative Property When tow numbers are added, the sum is the same regardless of the order of the addends. For example 4+2=2+4
Associative Property When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2+3)+4=2+(3+4)
Additive Identity Property The sum of any number and zero is the original number. For example 5+0=5
Distributive Property The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 x (6+3)=4 x 6 + 4 x 3
0/x=0 All intergers except 0
x-10x=-9x -9x=-9x All intergers
x2=-49 No solution is possible
(-x)3 Neither
Higher the power... lower in value
x+y=y+x Always true
x-y=y-x Sometimes True
x-y=x+y Sometimes True
xy=x+y Sometimes True
xy+x2=x(y+2) Always True
x . x=x2 Always True
x+x=x2 Sometimes True
x+y=x Sometimes True
x+1=x Never True
xy=yx Always True
x . 0=x Sometimes True
-(x-y)=-x-y Sometimes True
x0=0 Never True
x/y=y/x Sometimes True
1/x=0 Never True
3x+3=x+1 ---- 3 Always True
The difference between 2 even # is an an even # Always True
The product of any two even #'s is an odd # Never
The difference between any two odd numbers is an odd # Never
The product of any two odd # is a odd # Always
If x is greater than y, then 3x is greater than 3y Always
If x is greater than y, then x is greater than -y Never
Teh square of a number, x, is greater than x Sometimes
If 2x is greater than 2y, then x is less than y Never
Created by: DanceLots