Sample Spaces and Probability Addition Rules Multiplication Rules and Conditional Probability Counting Rules Probability and Counting Rules

Question If one card is drawn from a standard deck of cards, what is the probability of getting a spade?

Answer 1 – 10 13/52

Question If a die is rolled, what is the probability of getting a number greater than 2?

Answer 1 – 20 4/6

Question Human blood is grouped into four types. The percentages of Americans with each type are listed below: – O 43 – A 37 – B 12 – AB 5 If one American is chosen at random, find the probability of the person having type O blood?

Answer 1 – 30 43/97

Question Which statement(s) are true? P(E) = P(Ē) P(Ē) = P(E) 3.1 – P(E) = P(Ē) 4.P(E) + P(Ē) = 1

Answer 1 – 40 3, 4

Question What is the difference between classical and empirical probability?

Answer 1 – 50 Classical probability assumes all outcomes are equally likely Empirical probability is based on observation and experience

Question When two events A and B are mutually exclusive, what is the probability of A or B happening?

Answer 2 – 10 P(A) + P(B)

Question When two events A and B are NOT mutually exclusive, what is the probability of A or B happening?

Answer 2 – 20 P(A) + P(B) – P(A and B)

Question Which events are mutually exclusive? 1.Getting a 7 and a jack 2.Getting a club and getting a king 3.Getting a face card and getting an ace 4.Getting a face card and getting a spade

Answer 2 – 30 1, 3

Question A day of the week is selected at random. What is the probability that it is a weekend day?

Answer 2 – 40 2/7

Question A single card is drawn at random from an ordinary deck of cards. Find the probability that it is either an ace or a black card.

Answer 2 – 50 28/52

Question When two events A and B are independent, what is the probability that both A and B happen?

Answer 3 – 10 P(A) * P(B)

Question When two events A and B are dependent, what is the probability that both A and B will happen?

Answer 3 – 20 P(A) * P(B|A) OR P(B) * P(A|B)

Question Worldwide Insurance company found that 53% of the residents of a city had homeowner’s insurance (H) with the company. Of these clients, 27% also had automobile insurance (A) with the company. If a resident is selected at random, find the probability that the resident has both homeowner’s insurance and automobile insurance with Worldwide Insurance.

Answer 3 – 30 14%

Question Three cards are drawn from a deck. Find the probability of getting 2 aces and a king.

Answer 3 – 40 4/52 * 3/51 * 4/50

Question Suppose you draw 5 cards from a deck. What is the probability of drawing at least one heart?

Answer 3 – (39/52) 5

Question What is the difference between combinations and permutations?

Answer 4 – 10 Order matters for permutations, but not for combinations.

Question What is 7! ?

Answer 4 – 20 7*6*5*4*3*2*1 = 5040

Question Suppose a business owner has a choice of 5 locations in which to establish her business. She decides to rank her top 3 locations. How many ways can she rank them?

Answer 4 – 30 5 P 3 = 5!/(5-3)! = 5!/2! = 5*4*3

Question The Foreign Language Club is showing a four- movie marathon of subtitled movies. How many ways can they choose 4 out of the 11 movies?

Answer 4 – C 4 = 11!/7!4! = 11*10*9*8/4*3*2*1

Question How many ways can a dinner patron select 3 appetizers and 2 vegetables if there are 6 appetizers and 5 vegetables on the menu?

Answer 4 – 50 6 C 3 * 5 C 2 = 6*5*4/3*2*1 * 5*4/2*1

Question Find the probability of selecting 3 science books and 4 math books from 8 science books and 9 math books. The books are selected at random.

Answer 5 – 10 8 C 3 * 9 C 4 17 C 7

Question Find the probability that is 5 different sized washers are arranged in a row, they will be arranged in order of size.

Answer 5 – 20 5*4*3*2*1

Question Find the probability of getting a full house (3 cards of one denomination and 2 cards of another) when 5 cards are dealt from an ordinary deck.

Answer 5 – 30 4 C 3 * 4 C 2 52 C 5

Question If 50 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets.

Answer 5 – 40 2 C 2 50 C 2

Question A football team consists of 20 each freshmen and sophomores, 15 juniors, and 10 seniors. Four players are selected at random to serve as captains. Find the probability that 1.At least one of the captains is a senior. 2.There is 1 of each: freshman, sophomore, junior, senior

Answer 5 – – 55C4 65C C 1 * 20 C 1 * 15 C 1 * 10 C 1 65 C 4