A pair of fair dice are thrown 10 times. This question will be about a binomial distribution. Some event will be a “success” with probability p. Then calculate the probability that e.g. k = 3 or k ≤ 2 or k > 0. (a) What is the probability that the sum of the two dice is greater than 8 in exactly 4 of the 10 throws? (b) What is the probability that the sum of the two dice is greater tha

11. At a particular lake 4% of the fish have a disease which causes food poisoning. You go to the lake one day and catch 6 fish. Assume each fish in the lake has an equal chance of being caught. You eat all the fish you catch. What is the probability you get food poisoning? (a) 0.204 (b) 0.217 (c) 0.229 (d) 0.242

The proportion of male students at University of Yale is known to be 65%.  Assume students are randomly assigned to tutorial groups.  What is the probability that there would be fewer than 8 males in a tutorial group of 25 students? (4dp)  What is the probability that there would be more than 18 males in a tutorial group of 25 students? (4dp)

Suppose one NBA player can get one point in each free shot with probability 0.8. Now he has five times of free shots and it is reasonable to assume that the result in each shot has no impact on other shots. (b) What is the probability of his getting 3 points?(c) What is the probability of his getting at least 2 points?(d) we define an unusual event if the chance of the event is below 5%. Is it an unusual event that he lost all his shots? please explain each step fully

Overall, Steve Dalkowski throws a strike with 17% of his pitches (that is, the probability that he throws a strike with any given pitch is .17). (a) In one game, Dalkowski throws 240 pitches. What is the probability that he throws exactly 40 strikes? (b) In one week, Dalkowski throws 400 pitches. What is the probability that he throws 80 or more strikes? Every day for eternity Dalkowski throws 100 pitches, and records the number of strikes. (c) Find the mean µ, and the standard deviation o, of the numbers (of strikes thrown on different days) that Dalkowski records.

An instructor gives his class a set of 12 problems with the information that the next quiz will consist of a random selection of 4 of them. If a student has figured out how to do 9 of the problems, what is the probability the he or she will answer correctly  (a) all 4 problems? 0.2545(b) at least 3 problems.

Based on a survey, we assume that 59% of students have a pet. Suppose that there are 4 students sitting at a table. Find the probability of each of these events. Give each probability as a percentage rounded to two decimal places. (a) What is the probability that all 4 students have a pet? (b) What is the probability that none of the 4 students have a pet? % (c) What is the probability that at least one of the 4 students have a pet? % %