Suppose you roll 6 ’fair’ dice (each has six sides numbered 1 to 6 and each side has an equal 1/6 probability of showing). Let event A be the case where exactly two dice show a number less than 3 (1 or 2). Let event B be the case where where exactly two dice show a number greater than 4 (5 or 6)) Let event C be the case where every die shows a different number. a. What is probability of rolling the 6 dice and seeing both the A and B conditions? b. What is probability of rolling the 6 dice and seeing the C condition? c. What is probability of rolling the 6 dice twice and seeing the C condition in both rolls? Suppose you now roll 12 ’fair’ dice (not 6 dice rolled 2 times; you use 12 distinct dice) d. What is probability of seeing exactly 2 dice for each number (1 to 6)? e. Explain why the answer to d is the either the same or not the same as the answer to c?

The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender:   Opinion Female Male Almost no chance 120 94 Some chance but probably not 156 178 A 50-50 chance 427 498 A good chance 750 700 Almost certain 1176 770   How many individuals are described in this table? How many females were among the respondents? The percent of females among the respondents was about %. Your percent from the previous exercise is part of the marginal distribution of opinion about marriage. the conditional distribution of sex among adolescents with a given opinion. the marginal distribution of sex. What percent of females thought that they were almost certain to be married in the next 10 years?% Your percent from the previous exercise is part of the conditional distribution of sex among…

There are a total of 24 people in an application pool, that are equally qualified for a job. The pool consists of; 10 people from California 9 people from Nevada. 5 people from Arizonia.  There are 3 job openings for three different people. Type your answers as a decimal to 4 decimal places. 1. What is the probability that all three people are from California?    2. What is the probability that not all three people are from California?    3. What is the probability that none of the three people are from California?    4. What is the probability that one is from California and two are from Nevada?    5. What is the probability that the first one is from California and the next two are from Nevada?    6. What is the probability that each is from a different state?

Delta Airlines' flights from Boston to Dallas are on time 60 % of the time. Suppose 13 flights are randomly selected, and the number on-time flights is recorded.1.The probability that at least 9 flights are on time is =2.The probability that at most 8 flights are on time is =3.The probability that exactly 12 flights are on time is =