n B) I /57 P(A n B) = P(BA) x P(A) P(A) = n(s) P(A ) = 1 P(A)

Transcription

1 MDM4UIO1 WaterlooOxford District Secondary School Total: Mathematics Department Mrs. K. van Lierop Unit 3 Test Probability /57 Name: I4)lSwe (5 Date: Monday October 16, 2017 Theoretical Probability: P(A) = n(s) Probability of Complementary Event: P(A ) = 1 P(A) Additive Principle for Union of Two Sets: n(a u B) = n(a) + n(b) n(a Additive Principle for Probabilities: P(A U B) = P(A) + P(B) P(A n B) Additive Principle for Probability of Mutually Exclusive Events: P(A U B) = P(A) + P(B) Multiplication Law for Conditional Probability: P(A n B) = P(BA) x P(A) Multiplication Law for Independent Events: P(A n B) = F(A) x F(B) n B) I Multiple Choice (12 marks) Jdentfr the letter ofthe choice that best complees (lie statement or answers the question. 1. An experiment that models an actual event is a(n) a. trial c. simulation b. test d. experiment 2. An event occurs, on average, every 6 out of 17 times during a simulation. The experimental probability of this event is a. 11 c b. 17 d The collection of all possible outcomes of an experiment is called the a. event space c. outcome space b. probability space d. sample space 4. A bag contains 3 red blocks, 2 blue blocks, and 6 yellow blocks. If you draw one single block, then n(s) is a. 3 c. 6 b. I d Let set A be the set of face cards and B be the set of all spades in a regular deck of cards. State which statement is true. a. n(anb)=3 c. nc4nb)=l6 b. n(atib)16 d. n(a.b)=3 Page lof 6

2 Unit 3 Test Probability 1) 6. The probability of drawing a face card from a deck of cards is a. 1 c. 3 C / b. 4 d Find the probability that when a single card is drawn from a regular deck of cards a diamond or six is chosen. a. 17 c. 4 b d. noneoftheabove 8. Given that PU) 0.4. P(B) 0.5, and P(4t.. B) is 0.6, the value of PA nb) is a. 1.5 b. I c. 0.3 d. 0.1 A class is surveyed to determine whether they prefer Mathematics or English. The table below shows the results. Given that a sthdent is male, state the probability that mathematics is preferred. Gender Mathematics English Males 4 9 Females 7 8 a b c. 4 9 d. none of the above l0. Given the following Venn diagram, determine P A n B). a b C d. none of the above Page 2 of 6

3 Unit 3 Test Probability II. Identi which situation represents two dependent events. a. drawing two cards from a deck without replacement b. flipping a coin twice c. rolling a pair of dice one after the other d. none ofthe above 12. Identify the probability of rolling an even number on a regular six sided die. a.l c b. 1 d. none of the above 2 Short Answer (18 marks) 1) Determine the theoretical probability of each of the following events. Express yourflnal answer as afraction in lowest terms. Assume all questions involving cards make use of a shuffled, standard deck of 52 cards and all die are regular 6 sided die. [2 marks each] a) Rolling two six s two die. ±xfr J 3(o b) Rolling doubles with two die. in to c) Drawing a numbered club on the first draw and a numbered spade on the second draw from a deck of cards, without replacement S) 2IS2 LD1423 d) Drawing anything but a face card from a deck of cards, on the first draw. I LI] J I 3 e) Randomly pulling out 3 vowels in 3 draws, if each of the letters of the word Volkswagen are placed in a hat. 1 5 I2S 13 Page 3 of 6

4 a O0UPCk onsvjer jafscin C&(1?C±I o&sv Un ppsd9(i 9iAiuIa(c r Ot7U U a) Explain how you would do one trial.[3 marks] 2) An experiment is conducted using a deck of cards to simulate guessing on a multiple choice test that has four choices. Page 5 of 6 OjS6tO1Ott 1ob5 o1flq) I ob5)( qyo) (a3sth%( p(\(wl* (Lt(L [4 marksl a) The probability that it will win two out of its first three games. (a tree diagram may be helpful) is 65%, Determine the following; chance of winning if it wins the previous game. If the chance of winning its first game of the season 4) Statistics show that a team has a 30% chance of winning if it loses the previous game and a 60% H zsfl5 t mathematical proof.[5 marksj P((4n) the event that the red die shows a 2. Are these events independent? Support your answer with 3) Two dice, one red and one green are rolled. Let A be the event that the sum of the dice is 5. Let B be pbriixli1is dii 413 tl &jio/ejca/ prcthw/kos *Jb o j,io./s i iupoc?ypeiiiieii probabilities?[2marks] b) How would you make the experimental probabilities more similar to the theoretical wuc be ondcrn Unit 3 Test Probability

5 2) According to the following Venn diagram, 5/3 t)( qshdd5) 3 0 Choosing 4 students for a 5 person committee from a group of 12 students and 1 teacher. Page 4 of 6 15Cc P(FIfl 5flPIce) 3 heads is flipped, a five is rolled, and an ace is drawn. 13 marks] 1) A coin is flipped, a die rolled, and a card drawn from a regular deck. Determine the probability that formula, Tree Diagram ete). To earn full marks on these questions, you must show some related work (Vcnn Diagram, use of a Problems 123 marksl ii S 4VhU2IIj Snc, (AnnD) O pp flbncd) Determine if (A n B n D) is mutually exclusive. [2 marks] c) Determine the value of P(A n B n C). [2 marks] jd (Q b) What is the value of P(Ø? [1 mark] a) What is the value ofn(c)? [1 mark] Unit 3 Test Probability

6 Unit 3 Test Probability b) The probability of winning the last game given that they lost the first two games. marksj P( IN % hoi at Winni & /oyn ve 5) A veterinarian examines 60 pets for heartworm and dental disease. Of those 60 pets, 13 have heartworm. 33 have dental disease, and 1 7 have neither symptom. Some have both symptoms. Find the probability a pet selected at random has both heartworm and dental disease.j3 marksl nluv)h(1thc) nc\flo) I ofl I333 h(1tfld) 6) From a medical study of male patients, it was found that 2500 were smokers; 720 died from lung cancer and of these, 610 were smokers. Determine the probability of dying from lung cancer given being a nonsmoker. [4 marksj r non novlr Ccnctr \nsc:rtrn \uao P1 PCP) LQ nlti\y ZoIo ckiooooz 0,046 Bonus:[2marksj Determine the probability of a Straight Flush (5 consecutive cards of the same suit, but not including the Royal FLush). An ace can be used as a 1 or as the highest card, but you cannot wrap around a straight, i.e. JQKA2 is not a straight, A2345 is. Page 6 of 6