chapter 8 test: memorizing answers bc i don't know how to do the actual math
The probability that Marco leave his umbrella in any place he visits is 1/3. After visiting two friends in succession, he finds he has left his umbrella at one of his friends; places. What is the probability that he left his umbrella at the second friend's place?
2/5
In a group of 200 students taking the IB examination, 120 take Spanish, 60 take French, and 10 take both. a) If a student is selected at random, what is the probability that the student i) takes either French or Spanish. ii) takes either french or Spanish, but not both. iii) does not take either french or Spanish? b) given that a student takes Spanish, what is the chance that the student takes French?
i) 17/20 ii) 4/5 iii) 3/20 b) 1/12
In a factory producing computer disk drives, there are three machines that work independently to produce one of the components. In any production process, machines are not 100% fault free. The production after one batch from each machine is listed in the table. a) A component is chosen at random from the batches. Find the probability that the chosen component is: i) from machine one. ii) a defective component from machine 2. iii) non-defective or from machine one. iv) from machine one given that it is defective. b) is the quality of the component dependent on the machine used?
i) 63/185 ii) 2/185 iii) 178/185 iv) 3/10 b) 84/6845
A new blood test has been shown to be effective in the early detection of a disease. The probability that the blood test correctly identifies someone with a disease is 0.99, and the probability that the blood test correctly identifies someone without the disease is 0.95. The incidence of this disease in the general population is 0.0001. A doctor administered the blood test to a patient and the test result indicated that this patient had the disease. What is the probability that the patient has the disease?
0.001976
Communication satellites are difficult to repair when something goes wrong. One satellite uses solar energy and it has two systems that provide electricity. The main system has a probability of failure of 0.002. It has a back up system that works independently of the main one and has a failure rate of 0.01. What is the probability that the systems do not fail at the same time?
0.99998
The chance of rain on any day during the summer in Schaditz, Austria, is 0.2. When it rains, the probability that the daily maximum temperature exceeds 25 degrees C is 0.3, while it is 0.6 when it does not rain. Given that the maximum daily temperature exceeds 25 degrees C on a certain summer's day, find the probability that it rained on that day.
1/9
Asha walks to school every day. If it is not raining, the probability that she is late is 0.2. If it is raining, the probability that she is late is 2/3. The probability that it rains on any particular day is 0.25. Last Friday, Asha was late. find the probability that it was raining on that day.
10/19
Two events A and B have the conditions: P(A|B) = 0.30, P(B|A) = 0.60, P (A∩B) = 0.18. a) find P(B) b) are a and b independent? Explain c) Find P(B∩A')
a) 0.6 b) They are independent since P(B) = 0.6 = P(B|A). c) 0.42
In a survey, 100 managers were asked "do you prefer to watch the news or play sport?' Of the 46 men in the survey, 33 said they would choose sport, while 29 women made this choice. Fin the probability that: a) a manager selected at random prefers to watch the news b) a manager prefers to watch the news, given that the manager is a man
table (going across): 13, 25, 38, 33, 29, 62, 46, 54, 100 a) 19/50 b) 13/46
For events X and Y, P(X)= 0.6, P(Y)= 0.8 and P(X U Y) = 1. find: a) P(X ∩ Y) b) P(X' U Y")
a)0.4 b)0.6
In several ski resorts in Austria and Switzerland, the local sports authorities use senior high school students as ski instructors to help deal with the surge in demand during vacations. HOweve, to become a ski instructor, you have to pass a test and must be a senior at your school. Here are the results of a survey of 120 Students in a Swiss school who are training to become instructors. In this group, there are 70 boys and 50 girls. 74 students took the test, 32 boys and 16 girls passed the test, the rest including 12 girls failed the test. 10 of the students, including 6 girls, were too young to take the ski test. a) copy and complete the table b) find the probability that i) a student chosen at random, had taken the test. ii) a girl chosen at random has taken the test. iii) a randomly chosen boy and randomly chosen girl passed the ski test.
a) (goes across) 32, 16, 14, 12, 20, 16, 4, 6 b) i) 37/60, ii) 14/25, iii) 128/875
Many airport authorities test prospective employees for drug use. This procedure has plenty of opponents who claim that this procedure creates difficulties for some people and that it prevents others from getting these jobs even if they were not drug users. The claim depends on the fact that these tests are not 100% accurate. To test this claim, assume that a test is 98% accurate in that it correctly identifies a person as a user or non-user98% of the time. Each job applicant takes this test twice. The tests are done at separate times and are designed to e independent of each other. What is the probability that a) a non-user fails both tests b) a drug user is detected c) a drug user passes both tests
a) 0.0004 b) 0.9996 c) 0.0004
Roberto travels to school in a neighboring town by bus every weekday from Monday to Friday. The probability that he catches the 8:00 bus on any other weekday is 0.75. A weekday is chosen at random. a) Find the probability that he catches the 8:00 bus on that day. b) Given that he catches the 8:00 bus on that day, find the probability that the chosen day is Friday.
a) 0.732 b) 0.180
The independent events A and B are such that P(A)= 0.4 and P(A U B) = 0.88 Find: a) P(B) b) the probability that either A occurs, or B occurs, but not both.
a) 0.80 b) 0.56
For events A and B, the probabilities are P(A)= 3/11, P(B) = 4/11. Calculate the value of P(A∩B) if: a) P(A U B) = 6/11 b) events A and B are independent.
a) 1/11 b) 12/121
Two unbiased six-sided dice of different colors are rolled. find: a) P(the same number appears on both dice) b) P(the sum of the numbers is 10) c) P(the sum of the numbers is 10 or the same number appears on both dice)
a) 1/6 b) 1/12 c) 2/9
In a school of 88 boys, 32 study economics (E), 28 study History (H), and 39 do not study either subject. This information is represented in the Venn diagram. a) calculate the values a, b, and c. b) A student is selected at random. i) calculate the probability that he studies both Economics and history. ii) Given that he studies economics, calculate the probability that he does not study History. c) A group of three students is selected at random from the school. i) calculate the probability that none of these students studies economics. ii) calculate the probability that at least one of these students studies economics.
a) 11, 21, 17 b) i) 1/8 ii) 21/32 c) i) 0.258 ii) 0.742
Martina plays tennis. When she serves, she has a 60% chance of succeeding with her first serve and continuing the game. She has a 95% chance on the second serve. OF course, if both serves are not successful, she loses the point. a) find the probability that she misses both serves. If Martina succeeds with the first serve, her probability of gaining the point against steffy is 75%; if she is only successful with the second serve, the probability for that point goes down to 50%. b) find the probability that Martina wins a point against steffy.
a) 2% b) 64%
Antonio and Sarah play a game by throwing a dice in turn. If the dice shows a 3, 4, 5, or 6, the player who threw the dice wins the game. If the dice shows a 1 or 2, the other player has the next throw. Antonio plays first and the game continues until there is a winner. a) write down the probability that Antonio wins on his first throw. b) calculate the probability that Sarah wins on her first throw. c) calculate the probability that Antonio wins the game.
a) 2/3 b) 2/9 c) 3/4
Two events A and B are such that P(A) = 9/16, P(B) = 3/8, and P(A|B) = 1/4. Find the probability that: a) both events will happen b) only one of the events will happen c) neither event will happen.
a) 3/32 b) 3/4 c) 5/32
At a school, the students are organizing a lottery to raise money for their community. The lottery tickets that they have consist of small coloured envelopes containing a small note. The note either says "you won a prize" or "sorry try another ticket."The envelopes have several coulours. They have 70 red that contain two prizes and the rest (130) contain four other prizes. a) you want to help this class and you buy a ticket hoping it will not have a prize. You pick your ticket at random by closing your eyes. What is the probability that your ticket does not have a prize? b) You picked a red envelope. What is the probability that you did not win a prize.
a) 63/100 b) 34/35
Two fair dice are thrown and the number showing on each is noted. Find the probability that: a) the sum of the numbers is less than or equal to 7. b) at least one dice show s 3 c) at least one dice shows a 3, given that the sum is less than 8.
a) 7/12 b) 11/36 c) 1/3
Six balls numbered 1, 2, 2, 3, 3, 3, are placed in a bag. Balls are taken out one at a time from the bag at random and the number noted. Throughout the question a ball is always replaced before the next ball is taken. a) a single ball is taken from the bag. let X denote the value shown on the ball. Find E(X). b) Three balls are taken from the bag. Find the probability that: i) the total of the three numbers is 5. ii) the median of the three numbers is 1. c) ten balls are taken from the bag. Find the probability that fewer than four of the balls are numbered 2. d) find the fewest number f balls that must be taken from the bag for the probability of taking out at least one ball numbered 2 to be greater than 0.95. e) another bag also contains balls numbered 1, 2, or 3. eight balls are to be taken from this bag at random. it is calculated taht the expected number of balls number 1 is 4.8, and the variance of the number of balls numbered 2 is 1.5. Find the fewest possible number of balls numbered 3 in this bag.
a) 7/3 b) i) 7/72 ii) 2/27 c) 0.559 d) 8 e) 12/20
The Venn diagram shows a sample space U and events X and Y. n(U) = 36, n(X)= 11, n(Y)= 6 and n(X U Y')= 21. a) copy the diagram and shade the region (X U Y') b) find i) n(X ∩Y) ii) P(X∩Y) c) Are events X and Y mutually exclusive? Why or why not?
a) a picture b) i) 2. ii) 1/18 c) Events X and Y are not mutually exclusive since there are two elements in the intersection of the two sets: X ∩Y do not equal O.
In a survey of 200 people, 90 of whom were female, it was found that 60 people were unemployed, including 20 males. a) copy and complete table b) if a person is selected at random from this group of 200, find the probability that this person is: i) an unemployed female. ii) a male given that the person is unemployed.
a) going across 20, 40, 60, 90, 50, 140, 110, 90, 200 b) i) 1/5 ii) 9/14
Two girls, Catherine and Lucy, play a game in which they take turns in throwing an unbiased six-sided dice. The first one to throw a 5 wins the game. Catherine is the first to throw. a) find the probability that: i) Lucy wins her first throw. ii) Catherine wins on her second throw. iii) Catherine wins on her nth throw. b) Let p be the probability that Catherine wins the game. Show that p = 1/6 + 25/36p. c) Find the probability that Lucy wins the game. d) suppose that they play the game six times. Find the probability that Catherine wins more games than Lucy.
a) i) 5/36 ii) 25/216 iii) 1/6(5/6)^2n-2 b) 1/6 + 25/36 x p c) common ratio (5/6)^2. first term is 5/6 x 1/6 d) 1/9
The table below shows the subjects studied by 210 students at a college a) A student from the college is selected at random. let A be the event the student studies art. Let B be the event that the student is in year 2. i) find P(A) ii) Find the probability that the student is a year 2 art student ii) Are the events A and b independent ? b) Given that the history student is selected at random, calculate the probability that the student is in Year 1. c) Two students are selected at random from college. Calculate the probability that one student is in year 1 and the other is in year 2.
a) i) 8/21 ii) 1/6 iii) 10/21 b) 10/17 c) 200/399
Two independent events A and B are given such that: P(A) = k, P(B)= k+0.3 and P (A ∩ B)= 0.18. a) find k, b) find P(A ∪ B), c) P(A' | B')
a) k=.3 b) 0.72 c) .7
The Venn diagram shows the universal set U and the subsets M and N. a) copy the diagram and shade the area which represents the set M ∩ N'. n(U) = 100, n(M) = 30, n(N) = 50, and n (M U N) = 65. b) find n(N ∩ M'). c) An element is selected at random from U. What is the probablity that this element is in N ∩ M'?
a) picture b) 35 c) 0.35
Sophia is a student at an IB school. The probability that she will be woken by her alarm clock is 7/8. If she is woken by her alarm clock, the probability she will be late for school is 1/4. If she is not woken by her alarm clock, the probability she will be late for school is 3/5. let W be the event that Sophia is woken by her alarm clock. Let L be the event "Sophia is late for school" a) copy and complete the tree diagram. b) calculate the probability that Sophia will be late for school. c) given that Sophia is late for school, what is the probability that she was woken by her alarm clock.
a) picture b) 47/160 c) 35/47