please solve.
The mathematics faculty at a college consists of 4 professors, 9 associate professors, 6 assistant professors, and 8 instructors. If one faculty member is randomly selected, nd the probability of choosing a professor or an instructor. The probability is , (Type an integer or a fraction. Simplify your answer.) Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The sum of the probabilities of all possible outcomes in an experiment is 1. Choose the correct answer below. 0 A. This statement is false. To make this statement true, change "1" to "'3'. O B. This statement is false. To make this statement true, change "1" to "2'. O C. This statement is true. 0 D. This statement is false. To make this statement true, change "1" to "4". Determine whether the following statement is true or false. If the statement is false. make the necessary change(s) to produce a true statement. If an experiment is repeated more and more times, the theoretical probability of an event tends to get closer to the empirical probability of that event. Choose the correct answer below. 0 A. The statement is false. The true statement is "If an experiment is repeated more and more times, the empirical probability of that event tends to get closer to 1.\" O B. The statement is false. The true statement is "If an experiment is repeated more and more times, the empirical probability of an event tends to get closer to the theoretical probability of that event." 0 C. The statement is true because the theoretical probability of an event tends to get closer to the empirical probability of that event when an experiment is repeated more and more times. 0 D. The statement is true because if an experiment is repeated more and more times, the proportion of outcomes favorable to any particular even tends to get closer to the theoretical probability of that event. A6sided die is rolled. The set of equally likely outcomes is {1 ,2,3,4,5,6}. Find the probability of rolling a number less than 9. The probability of rolling a number less than 9 is E. (Type an integer or a simplied fraction.) Use the spinner shown to answer the question. Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again. If the spinner is spun once, nd the probability that the pointer lands in a red region. The probability that the pointer lands in a red region is (Type an integer or a simplied fraction.) Sergio, Sarah, Larry, Kim, and Katrina have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. a. In how many ways can they arrive? b. In how many ways can Sergio arrive first and Katrina last? c. Find the probability that Sergio will arrive first and Katrina last. a. (Type an integer.) b. (Type an integer.) (Type a fraction. Simplify your answer.)A city council consists of six Democrats and seven Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans. (Type a fraction. Simplify your answer.)Use the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on purple grey and then purple purple grey Find the probability that the spinner will land on grey and then purple. (Type an integer or a simplified fraction.)The mathematics faculty at a college consists of 4 professors, 9 associate professors, 6 assistant professors, and 8 instructors. If one faculty member is randomly selected, nd the probability of choosing a professor or an instructor: The probability is . (Type an integer or a fraction. Simplify your answer.) Use the spinner shown to answer the question. Assume that it is equally probable that the pointer will land on any one of the colored regions. If the pointer lands on a borderline, spin again. If the spinner is spun once, find the probability that the pointer lands in a red region. red green green red red yellow The probability that the pointer lands in a red region is. (Type an integer or a simplified fraction.)
