Consider the experiment of throwing a dart at a circular dartboard of radius 1. Assume that in the experiment, the dart always hits the board, and the probability of the dart hitting a given region is proportional to the area of that region. (a) Find a mathematical description for the sample space in this experiment. (b) Fin
Consider the experiment of rolling two fair 6-sided dice. The outcome of the experiment will be used to play a game in which a player's piece advances by the total of the two dice. (a) Set up a probability space which accurately models this experiment. (b) Write down, as a set, the event that the sum of the two dice is 5. Fi
Let (S, E, P) be a probability space. (a) Let A <- E be an event such that P(A) = 0. Does it follow that A = PHI? If not, what can you say about A? (b) Prove that if A, B <- E, then A INTERSECTION B <- E and A - B <- E.
Please assist with the steps required to resolve the three statistical problems below? 1. In your own words, describe two main differences between classical and empirical probabilities. 2. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between
Find the indicated probability The table shows the number of college students who prefer a given pizza topping. Topping Freshman Sophomore Junior Senior Cheese 15 10 29 19 Meat 19 19 10
type of accommodation number house 676 flat 624 apartment 670 other 333 a survey resulted in the sample data in the given table. If one of the survey respondents is selected at random find
The age distribution of students at a community college is given below: age(years) number of students(f) under 21 407 21-25 407 26-30 200 31-35 31 over 35 23 ---------------------------------------------- 1088 A student from the comm
Consider the experiment of choosing a whole number between 1 and 10, where the probability of selecting a number is proportional to the number itself; for example, the outcome 4 is twice as likely as the outcome 2, etc. Set up an appropriate probability space to model this experiment. Be as explicit as possible.
I have 2 problems. Both are attached in the file 1. Consider the experiment of choosing a whole number at random from between 1 and 10, inclusive. a. Set up a sample space for this experiment. b. What is the event that the outcome is odd? Write your answer as a set. c. What is the event that the outcome is strictly g
Which of the following probabilities for the sample points A,B,and C could be true if A, B and C are the only sample points in an experiment? a- P(A)= 1/8, P (B) = 1/7, P(C)= 1/10 b. P(A)= 1/4 P(B)=1/4, P(C)=1/4 c. P(A)= -1/4, P(B)= 1/2 P(C)=3/4 d. P(A)=0, P(B)= 1/14, P(C)=13/14.
2. Two fair dice are rolled. Find the probability that the sum of the two numbers is not greater than 5. 3. This spinner is spun 36 times. The spinner landed on A 6 times, on B 21 times, and on C 9 times. Compute the empirical probability that the spinner will land on B. 4. If a person is randomly selected, find the probab
Lottery One million tickets are sold for a lottery in which a single prize will be awarded. a) If you purchase a ticket, determine your odds against winning. b) If you purchase 10 tickets, determine your odds against winning.
Please refer to the uploaded file.
Suppose you are flying a four-engine aircraft on a 10-hour transoceanic flight. Assume that it has been established that the probability of an engine of the type you have on your aircraft failing during a 10-hour flight is 0.008. Determine the probability of all four engines failing during the flight. A student decided that
The grade distribution is as follows for the past three (3) years for a course in college algebra, as shown below. A's - 45; B's- 180; C's - 110; D's - 95; F's - 65; and Incompletes- 5. If Jane plans to take a college algebra course, determine the empirical probability that she does not receive an F.
The average time taken to produce a part at Factory A is 10 minutes. Given this, find the following probabilities. a) The probability that at most 7 minutes is taken to produce the part. b) The probability that between 5 and 15 minutes are taken to produce the part. c) The probability that at least 3 minutes is taken to pro
6) The daily rate of production of a part is normally distributed with mean 75 and standard deviation 10. If denotes a day's production of this part, use this information to find the following probabilities. You may use computer software if you wish. (5 points each) a) P (X less than or equal to 90) b) P(55 less than
A country road averages 6 potholes per mile. A road crew is sent out to repair the road. Find the following probabilities. Use the appropriate table or software if you want. a) That a mile stretch of road will have exactly 7 potholes. (3 points) b) That a half mile stretch of road will have at most 2 potholes. (6 points)
4) 55% of a restaurant's orders are from customers eating in the restaurant and 45% from the drive through window. 65% of the orders from the customers eating in the restaurant are from food and 35% from drinks. 79% of the drive through orders are from food and 21% from drinks. Use this information to find the following probabi
1. In a poll, respondents were asked whether they had ever been in a car accident. 157 respondents indicated that they had been in a car accident and 117 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car
1. Business College is planning an online MBA tech program, start up cost for equipment, facilities, course development, staff recruitment and development is $350,000. College plans to charge tuition of $18,000 per student per year. The university administration will charge the college $12,000 per student for the first 100 stu
1) Tire Life - The life of a tire is normally distributed with a mean of 76,000 miles and a standard deviation of 10,000 miles. a) Determine the probability that a tire will last for less than 67,000 miles. b) Determine the probability that a tire will last for more than 67,000 miles. c) Determine the probability
1. How many rectangles are there in a line of fifteen squares where sides are lined up with the adjacent sides touching the entire length of the side? 2. If all the diagonals of a regular pentagon are drawn, how many triangles are formed? 3. If a 75-degree sector of a circle rotates around the center of a circle in 75-de
Evaluate the expression. Sec 12.6 #40 TWO Spins: assume that the pointer cannot land on the line and that each spin is independent. 40) Red and then yellow. Sec 12.9 #12 Evaluate the expression. a) b)
5.62 A certain airplane has two independent alternators to provide electrical power. The probabilitythat a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) On e or the other will fail? Show all steps carefully. 5.70 The probability is
7. Let A(4,3) and B(7,11) be two points in a plane. If all paths are equally likely, what would be the probability of choosing a path that begins with an up move and ends with an up move? (Each path is made up of moves that either go up one unit or over one unit to the right.) 8. In a state lottery game, anyone who picks 6 n
4. What are the odds that a randomly selected number between 1 and 100 will not have a digit 7? (For instance, 23 does not have a digit 7, but 73 does.) 5. There are 4 slots, each containing any of letters a, m, h, t. HINT: What are the odds that letters stored in these slots read the word math? Remember that each slot
What is a probability and what is a probability distribution? Explain with examples?
What "real world" factors do you think contribute to a skewed distribution? Please explain in detail.
A young girl gave a young man her phone number during a hurried parting. The young man remembers the 7 digits of her phone number, but in his emotional state he does not remember the order of the digitals. He decided to try to dial the seven digits in some random order. What is the probability that he will get to the right gi