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ASU / Math / MAT 211 / What is probability in math?

# What is probability in math? Description

##### Description: This study guide covers chapters 6.3 & 6.4, 7.1 to 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3, 8.4, 8.5, P.1, P.2 and P.3
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MAT 211 Final Exam Study Guide- Abramson’s Class  **Final will be on chapters 6.3 & 6.4, 7.1 to 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3, 8.4, 8.5, P.1, P.2 and P.3

## What is probability in math? 1) FCP, Permutations, Combinations, 7- letter sequence (6.3 & 6.4)

a. Ex FCP: 4 Appetizer, 10 main courses, 3 salads, 5 deserts. How many 3 course meals  are possible, order either appetizer or salad NOT both. (when there is “either, or” it  means addition) Don't forget about the age old question of thaght

Answer: (4 x 10 x 5) + (3 x 10 x 5) = 200+150= 350 course meals

b. Ex Permutation: P(5,3) to order 5 objects 3 at a time. (On Calc: Math????Prob????#2) Answer: P(5,3)= 5 x 4 x 3= 60 If you want to learn more check out math 266 iowa state

c. Ex Combination: C(5,3)???? 5 objects, choose 3 at a time. (On Calc: Math????Prob????#3) Answer: C(5,3)= (5x4x3)/(3x2x1)= 10

## (4 x 10 x 5)+(3 x 10 x 5) = 200+150 the answer is? d. Ex 7 letter strings: How many “strings” can be formed from “a,b,c,d,e,f,g”, no  repetition of letters.

i. 7 letter string 7 x 6 x 5 x 4 x 3 x 2 x 1= 5,040 = P(7,7)

ii. 5 letter string 7 x 6 x 5 x 4 x 3= 2,520 = P(7,5)

iii. 7 letter strings, but “c” must be the 2nd letter 6 x 1 x 5 x 4 x 3 x 2 x 1= 720 iv. 7 letter strings, but “a” must come before “b” ???? 7!/2= 2520

2) Probability- marbles, lottery (7.1-7.4) and Independent Events word problems (7.5) a. Ex Bag of Marbles ???? 3 red, 4 green, 2 white, 3 pink; grab 7 marbles

## P(5,3)= 5 x 4 x 3 the answer is? i. P(all red marbles)= [C(3,3)*C(9,4)]/C(12,7)= 7/44

ii. P( don’t have all the red marbles)= 1- P(opposite)= 1-(7/44)= 37/44 If you want to learn more check out What is modernism?

b. Ex Lottery: Lottery number 0 to 30 (there is 31 numbers total) select 6 numbers (order does not matter because as long as the numbers fill up 6 spaces), no  repetition.

i. P( all 6 #’s match)= n(s)/n(t)= 1/C(31,6)= 1/736,281

ii. P( 5 of 6 #’s match)= [C(6,5)*C(25,1)]/C(31,6)= 150/736,281

c. Ex Independent Events: P(A|B)= 0.4, P(B)= 0.6, P(A∩B)=? We also discuss several other topics like épn

Answer: P(A|B)= P(A∩B)/P(B)???? 0.4= X/0.6 ???? 0.4(0.6)= 2.4

d. Ex Independent Events Word problems: D= democrats and R= republicans; F= for  death penalty F’= against death penalty; P(R)= 0.6, P(F|D)= 0.7, P(F’|R)= 0.4

i. P(F’|D)= 0.3

ii. P(D∩F’)= 0.12

iii. P(R∩F)= 0.36

3) Bayes (7.6), Probability Distributions (8.1), Bernoulli (8.2), Z-scores (8.5) a. Ex Bayes: P(A|B)= 0.4, P(B)= 0.1, P(A|B’)= 0.15. Find P(B|A) and P(B|A’). Formula: given/possible outcomes

P(B|A)= .04/(0.4+.135)= 8/35 We also discuss several other topics like uccs math

P(B’|A’)= .765/(.06+.765)= 51/55

b. Ex Bayes word problem: P(Democrat)= 0.4, P(F|D)= 0.3, P(F|R)= 0.8. Find P(D|F),  P(R|F’), and P(F’|D).

P(D|F)= .12/(.12+.48)= .12/.60= 1/5 P(R|F’)= .12/(.28+.12)= .12/.40= 3/10

P(F’|D)= 0.7 (NOT Bayes Theorem???? just read

directly off of tree diagram)

c. Ex Probability Distributions: Roll two die, x= square of sum of #’s on 2 die. Find the  probability. P(x=9)= 2/36

P(x=64)= 5/36

P(x=3)= 0

P(x>40)= (6+5+4+3+2+1)/36= 21/36

P(25<= x<100)= (4+5+6+5+4)/ 36= 24/36 If you want to learn more check out matthew hoddie

P(x>.5)=1

P(x<3)= 0

d. Ex Bernoulli Trials: Perform 5 Bernoulli Trials, p=0.2 Find x=2

e. Ex Z-Scores: 4) Mean, Median, Mode & Expected Value (8.3), Standard Deviation and Variance (8.4) a. Ex Standard Deviation and Variance: 5) Probability Density Functions (P.1, P.2, P.3)

a. Expected Value E(x), Standard Deviation of PDF (P.3) b. Free response question of f(x) PDF ???? yes, no (P.2) c. Probability a failing business will last 2 to 5 years or more than 3 years (P.2) d. Exponential Decay Functions (P.3) Page Expired It looks like your free minutes have expired! Lucky for you we have all the content you need, just sign up here
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