# Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II??

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1 Quiz 2 Review - on Notebook Paper Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n What are the formulas? Pr ncr Fill in the notation Intersection of two sets (A B) : Fill in the vocab. Union of two sets (A B) : Factorial: For any integer n>0, n! =n(n-1)(n-2)(n-3) (3)(2)(1) If n=0, 0! = Ex: 4! = If A and B are Independent events, then P(A and B) = P(A B) = If A and B are Dependent events, then P(A, then B) = Compliment of a set: P(not A) = P( ) = If A and B are Mutually Inclusive or Exclusive Events P(A or B) = P(A B) = If A and B are Conditional Events P(A given B) = P(A B) =

2 Quiz 2 Review KEY Are You Ready For Your Last Quiz In Honors Math II?? Some things to Know, Memorize, AND Understand how to use are n P r n! ( n r)! n C r n! ( n r)! r! Factorial: For any integer n>0, n! =n(n-1)(n-2)(n-3) (3)(2)(1) If n=0, 0! =1 Ex: 4! = Intersection of two sets (A B) : All the elements that appear in both sets (the overlap of the two sets) Union of two sets (A B) : Everything in either set (the items in A or B alone or both) Compliment of a set: all elements in the universal set that are NOT in the initial set P(not A) = P(A C ) = 1 - P(A) If A and B are Independent events, then P(A and B) = P(A B) = P(A) P(B) If A and B are Dependent events, then P(A, then B) = P(A) P(B after A) **assume success on 1 st draw** If A and B are Mutually Inclusive or Exclusive Events P(A or B) = P(A B) = P(A) + P(B) P(A B) If A and B are Conditional Events P(A given B) = P( A B) P(A and B) PB ( )

3 Whiteboard Review You will need: - Whiteboard - Marker - Eraser - Your brain!

4 A committee is to be formed consisting of 1 freshman, 1 sophomore, 2 juniors, and 2 seniors. How many ways can this committee be formed from 5 freshmen, 5 sophomores, 8 juniors, and 10 seniors? C C C C ,500

5 A local telephone number consists of 7 digits, and the first number cannot begin with 0 or 1. How many different local telephone numbers are possible? ,000,000

6 How many distinguishable ways can the letters in CASTRO be written? 6! = 720

7 How many distinguishable ways can the letters in MISSISSIPPI be written? 11! (4!4!2!) 34,650

8 How many different 7 card hands are possible from a standard 52 card deck? 52 C 7 = 133,784,560

9 2 coins are tossed. What is the probability of getting at least one tail? HH HT TH TT 3/4 Write as a fraction.

10 Write as a fraction. 4 coins are tossed. What is the probability of getting at least 3 tails? 5/16

11 From a standard deck of 52 cards, find the probability of getting a club, or a face card Write as a fraction.

12 John moves to Thailand, and only speaks English. On his first day of school he is given a 10 question multiple choice quiz in Thai, each with 4 options. What is the probability that John will guess all 10 questions correctly? (1/4) 10 = 9.5 x 10-7

13 A bag contains 3 blue, 4 purple, and 5 red marbles. 3 marbles are drawn. Find the probability of drawing: a) 2 red and a blue b) a blue, given you drew 2 reds a) 3/22 b) 3/10 Possibilities: red, red, blue (1/22) blue, red, red (1/22) red, blue, red (1/22) Write as a fraction.

14 A dice is rolled. Find the probability of rolling a number that is less than 5, or even Write as a fraction.

15 A store sells T-shirts in 5 colors, 9 designs, and 3 sizes. How many different T-shirts are available? 5 x 9 x 3 = 135

16 The odds of an event occurring are 15 to 7. What is the probability of the event occurring? 15/22 Write as a fraction.

17 A high school basketball team leads at halftime in 45% of the games in a season. The team wins 75% of the time when they have a halftime lead, but wins only 9% of the time when they do not have a halftime lead. Write as a percent. Round to the nearest tenth. a) What is the probability that the team wins a particular game during the season? 38.7% b) P(lose) 61.3% c) P(Does not lead win) 12.8% d) P(Leads lose) 18.4% e) Does not lead and wins 4.95%

18 Of 100 students, 23 are taking Calculus, 29 are taking French, and 12 are taking both Calculus and French. If a student is picked at random, what is the probability that the student is taking Calculus or French? 40/100= 2/5

19 In a student body election, there are three candidates for president, four candidates for vice president, and five candidates for secretary. How many possible groups of officers are there? 3 x 4 x 5 = 60 OR C C C

20 Extra Practice (if not completed)

21 Given the following Venn Diagram, how many students are taking an art AND a music class?

22

23 Given the following Venn Diagram, how many students are taking an art OR a music class?

24

25 Given the following Venn Diagram, how many students are in the Venn Diagram?

26

27 Given the following Venn Diagram, find the PROBABILITY that a student is taking an art AND a music class. P(art AND music) =

28 6 / 140 or 3 / 70

29 Given the following Venn Diagram, find the PROBABILITY that a student is taking an art OR a music class. P(art OR music) =

30 38 / 140 or 19 / 70

31 The probability of an event + the probability of its complement = P(A) + P(A C ) =

32

33 The probability of rain tomorrow is 40%. What is the probability that it doesn t rain?

34

35 The probability of rain tomorrow is 40%. What are the odds of rain?

36 4:6 or 2:3

37 At SWGHS, 30% of the students are sophomores. 48% of the students are female. What is the probability that a student is a female AND a sophomore?

38 14.4%

39 A coin and a die are tossed/rolled. What is the probability of getting tails and a 4.

40 1/12

41 If the probability of receiving a piece of mail is 25% on any given day, what is the probability of receiving a piece of mail today and no mail tomorrow?

42 18.75%

43 Given a standard deck of cards, what is the probability of drawing a diamond?

44 25%

45 Given a standard deck of cards, what is the probability of drawing a king?

46 1/13

47 Given a standard deck of cards, what is the probability of drawing the king of diamonds?

48 1/52

49 Given a standard deck of cards, what is the probability of drawing a king OR a diamond?

50 16/52 or 4/13

51 Given a standard deck of cards, what are the ODDS of drawing a diamond?

52 13:39 or 1:3

53 Tonight s Homework Packet p. 12 and 13 Omit problem #1 & 2 for now Study for Quiz Tomorrow!

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