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.

Answer:  

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?

Answer:

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.

Answer:

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

Answer:

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 

Answer:

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).

Answer:

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.

Answer:  

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

Answer: C(5,2) (0.2)2(0.8)3= 128/625

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)