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- A box of 6 cellphones contains three yellow cellphones and three green cellphones. Complete parts (a) through (d) below. a. If two cellphones are randomly selected from the box without replacement, what is the probability that both cellphones selected will be green? P(both green) = (Round to four decimal places as needed.)2.) In a class with 13 undergraduates and 10 graduate students, a 4-member panel will be randomly chosen. Find the probability that the group contains the following, and round your answer to 4 decimal places. (a) 2 graduate students and 2 undergrads (b) No more than 2 graduate studentsA box contains 10 marbles, 4 of them are white. We pick 5. Variable X represents number of white marbles. a) Calculate the probability distribution of variable X. b) What is the probability that at least 3 of picked marbles will be white? c) Calculate median of variable X.
- 3. An urn contains 10 red, 15 blue and 25 green balls. (a) Eight balls are chosen without replacement. What is the probability exactly 4 of the chosen balls are green? (b) Now four balls are chosen from the urn without replacement. What is the probability the first chosen ball is red, the second chose ball is green, the third chosen ball is green and the fourth chosen ball is blue?In a hall, one row has 20 seats. The GSI randomly permutes 20 students into those 20 seats. a) Students A and B are among the 20 students in the row. Find the decimal value of the expected number of students sitting between them. b) The 20 students in the row include 7 Data Science majors. Find the expected number of Data Science majors who are not seated next to another Data Science major. You don't have to find the decimal value.Here are three pieces of information about a few different populations where we are interested in the proportion who vote "green". In each of the data, you must determine the probability that the sample share ports are a maximum of 7 percentage points * from the population share. A) The population consists of 6 people, of which 3 people vote "green". The sample consists of 2 people. b) The population consists of 200 people, of which 90 people vote "green". The sample consists of 10 people. c) The population consists of 10,000 people, of which 4200 people vote "green". The sample consists of 200 people. * Example: In the a-task, “the sample share ends up with a maximum of 7 percentage points from the population share” means that the sample share ends up between 43% and 57%. Explain a, b, c
- 5) Samples of size n = 2 are randomly selected with replacement from the popula- tion consisting of 2, 4, and 10, where the values represent the number of people in households. 5a) Find the mean of each of the nine samples and summarize the data in the form of a probability distribution. seroMvT as borolgo olgouq Ind upo o t te bas io 5b) Compare the population mean to the mean of the sample means in this example. Does this support the idea that sample means do not target the population means?5. A bucket contains 7 red balls, 8 green balls, and 5 black balls. If 4 balls are chosen randomly, find the probability that at least 1 of them is red. (6A shipment of 11 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 11, will not contain a defective computer. ..... The probability is (Type an integer or a simplified fraction.)
- 7. There are four tickets in a box, numbered from 1 to 4. We draw two without replacement. What is the probability of getting a "1" and a "“2" (in no particular order).A box contains 100 agricultural products, 30 of which are defective. Three products are selected at random without replacement from the box. i) Find the probability that the first one is defective. ii)Find the probability of third one is defective given that the first two are good. iii) Find the probability of three defective.Determines the number of subsets of any size in a set of 25 elements From the subsets of the previous part, one is going to be selected at random, what is the probability that it has 2 elements?