Here are some problems from my math lab that I need help with. Problem number 5# Eleven of the 50

digital recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective? The probability is ---- (Do not round). problem # 6 Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing an odd number between 1 and 9, inclusive The sample space is---- (Use a comma to separate answers as needed. Use ascending order.) so there are ---- outcomes in the sample space. problem#7. A software company is hiring for two positions: a software development engineer and a sales operations manager. How many ways can these positions be filled if there are 19 people applying for the engineering position and 18 people applying for the managerial position? The position can be filled in ---- ways. problem#9. Consider a company that selects employees for random drug tests. The company uses a computer to randomly select employees numbers that range from 1 to 5839. Find the probability of selecting a number less than 1000. Find the probability of selecting a number greater than 1000. The probability of selecting a number less than 1000 is--(Round to three decimal places as needed.) The probability of selecting a number greater than 1000 is---(Round to three decimal places as needed.) problem #10. Consider a company that selects employees for random drug tests. The company uses computer to randomly select employee numbers that range from 1 to 6282. Find the probability of selecting a number less than 1000. Find the probability of selecting a number greater than 1000. The probability of selecting a number less than 1000 is--- round to three decimal places as needed. The probability of selecting a number greater than 1000 is--- round to three decimal places as needed. problem #11. A probability experiment consists of rolling a eight sided die and spinner shown at the right. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the given event. Then tell whether the event can be considered unusual. Event: rolling a number less than 3 and the spinner landing on yellow the probability of the event is --- ( type an integer or decimal rounded to three decimal places as needed.) Can the event be considered unusual? problem #12. Use the frequency distribution, which shows the responses of a survey of college students when asked, "How often do you wear a seat belt when riding in a car driven by someone else?" Find the following probabilities of responses of college students from the survey chosen at random. Response -- Never with the frequency of 117, rarely-- frequency 344, sometimes-- frequency of 569, most of the time with the frequency of 1372, always with the frequency of 2591, complete the table below for the response and the probability 1. never is response and the probability would be--- round to the nearest thousandth as needed. 2. response is rarely and the probability would be--- round to the nearest thousandth as needed. 3. response is sometimes and the probability would be--- round to the nearest thousandth as needed 4. response is most of the time and the probability would be--- round to the nearest thousandth as needed. 5. response is always and the probability would be--- round to the nearest thousandth as needed. problem #13. Use the pie chart at the right, which shows the number of tulips purchased from a nursery. Find the probability that a tulip bulb chosen at random is red the red tulip bulbs are 30 the probability that a tulip bulb chosen at random is red is--- (do not round). problem#14. Use the pie chart at the right, which shows the number of workers (in thousands) by industry for a certain country. Find the probability that a worker chosen at random was not employed in the mining and construction industry. Agriculture, forestry, fishing and hunting 2981, services 115,861, manufacturing 16,055, and mining and construction 11,103. The probability is---.(round to three decimal places as needed.) problem #15. In gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to"3) or 2/3. (Note: If the odds of winning are 2/3, the probability of success is 2/5.) The odds of an event occurring are 5:1. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. The probability that the event will occur is---. (type an integer or decimal rounded to the nearest thousandth as needed.) The probability that the event will not occur is---(type an integer od decimal rounded to the nearest thousandth as needed.) problem#16. The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or 2-3. A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a 2 of spades. The odds that it is a 2 of spades are---:--- (Simplify your answer). problem #17. In the general population, one women in eight will develop breast cancer. Research has shown that 1 women in 650 carries a mutation of the BRCA gene. Eight out of 10 women with this mutation develop breast cancer. (a) Find the probability that a random selected woman will develop breast cancer given that she has a mutation of the BRCA gene. The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is---(round to one decimal place as needed.) (b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer. The probability that a randomly selected woman will carry the gene mutation and develop breast cancer is ----(round to four decimal places as needed.) problem# 18. Suppose 80% of kids who visit a doctor have a fever, and 35% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat? the probability is--- (round to three decimal places as needed). problem#19. According to Bayes' Theorem, the probability of event A, given that event B, as occurred, is as follows. P( A| B)= P(A) . P(B|A) over P(A). P(B|A)+ P(A') . P(B|A') Use Bayes' Theorem to find P(A|B) using the probabilities shown below. P(A)=2/3, P(A') =1/3, P(B|A)=1/10, and P(B|A')=1/2 The probability of event A, given that event B has occurred, is P(A|B)=---- (round to the nearest thousandth as needed). problem # 20. Determine the probability that at least 2 people in a room of 9 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions: (a). the probability that 9 people have different birthdays is---(round to four decimal places as needed). (b) the probability that at least 2 people share a birthday is--- (round to four decimal places as needed). problem 21. By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B|A)= P(A and B)/ P(A). Use the information below to find the probability that a flight arrives on time given that it departed on time. The probability that an airplane flight departs on time is 0.91, the probability that a flight arrives on time is 0.88, the probability that a flight departs and arrives on time is 0.81, the probability that a flight arrives on time given that it departed on time is----(round to the nearest thousandth as needed) problem #25 The table below shows the results of a survey that asked 2864 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (c). frequently for male---225, for female 206 total for frequently is 431. occasionally for male is 456, female is 440 total is 896, for not at all male is 796, female is 741 total for this one is 1537, totals for male 1477, female1387 and the total is 2864, (a). Find the probability that the person is frequently or occasionally involved in charity work. P(begin frequently involved or being occasionally involved)=---(round to the nearest thousandth as needed for all of them.) (b). Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved)=--- (c) Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved)=---(d) Find the probability that the person is female or not frequently involved in charity work. P(being female or not frequently involved)=---(e). Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain. problem # 26. Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 56P2=-- problem # 27. Perform the indicated calculation is 6P3/10P4=--- (round to four decimal places as needed). problem # 28. Perform the indicated calculation. 9C3/13C3=---(round to the nearest thousandth as needed). problem #30. Outside a home, there is a 9-key keypad with letters A,B,C,D,E,F,G,H, and I that can be used to open the garage if the correct nine letter code is entered. Each key may be used only once. How many codes are possible? The number of possible code is----. problem #31. A golf course architect has six linden trees, four white birch trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a row, assuming that the trees are evenly spaced? The trees can be planted in --- different ways. problem # 32. Shuttle astronauts each consume an average of 3000 calories per day. One meal normally consist of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 10 main dishes, 7 vegetable dishes, and 12 desserts. How many different meals are possible? The number of different meals possible is----.problem #33. A basket contains 9 eggs, 3 of which are cracked. If we randomly select 4 of the eggs for hard boiling what is the probability of the following events?( A.) All cracked eggs are selected. (B). None of the cracked eggs are selected. (C). Two of the cracked eggs are selected. (a). the probability that none of the cracked eggs are selected is---- (b). the probability that none of the cracked eggs are selected is---- (c) the probability that two of the cracked eggs are selected is--- (Round all of them to four decimal places as needed.)