7 How many ways can 5 tickets are selected from 40 tickets if

each ticket wins a different prize.

8 How many ways can an adviser choose 5 students from a class

of 20 if they are all assigned the same task? How many ways

can the students be chosen if they are each given a different

task.

9 An investigative agency has 8 cases and 4 agents. How many

different ways the cases be assigned if only one case assigned

to each agent.

10 How many different 3 letter permutations can be formed from

the letters in the word "UNIVERSAL".

11 How many ways can a jury of 5 women and 5 men be selected

from 10 women and 15 men.

12 There are 15 seniors and 20 juniors in a particular social organization. In how many ways can 4 seniors and 3 juniors be

chosen to participate in a charity event.

13 How many ways can a person select 6 televisions commercials

from 12 television commercials.

14 How many ways can a person select 5 DVDs from a display of

12 DVDs.

15 How many ways can a buyer select 7 different posters from 20

posters

Medical case histories indicate the different illnesses may produce identical symptoms. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any

of three illnesses A, B or C occurs. (Assume and ) are mutually exclusive. Studies show these probabilities of getting the

three illnesses

P A^ ^ h h = 0.01, P B = 0.005, P C^ h = 0.02.

The probabilities of developing the symptoms H, given a specific illness are

P H( | A) 0 = .9, ( P H | ) B P = 0.95, ( | H C) 0 = .75.

Assuming that an ill person shows symptoms H. Find the

probability that the person has illness A. i.e. find P A_ i | H

2 A space of elementary events S can be divided into two

events E1

, E2 that occur with probabilities 60% and 40%

respectively. An event A occurs 30% of the time in the

first event E1 and 50% of the time in the second event E2

.

What is the unconditional probability of the event A, regardless of which event it comes from.

3 There are two boxes, the first one contains 4 white balls, and

6 black balls and the second one contains 8 white balls and 3

black balls. If we choose one box at random and take a ball

from it randomly, find the probability that:

a The chosen ball is black.

b If the chosen ball was black find the probability of getting

it from the first box.

4 A factory has three machines I, II, III. If machine I produces

20% of the items, machine II produces 30%, and machine III

produces 50% of the items, with defective from the machine as

5%, 2% and 1% respectively. If an item is selected at random,

find the probability that the item is not defective.

5 A manufacturer makes two models of an item, model I, which

accounts for 80% of units sales and model II, which accounts

for 20% of units sales. Because of defects, the manufacturer

has to replace 10% of its model I and 18% of its modelII. If a

model is selected at random. Find the probability that it will

be defective

Chapter 6 Continuous Probability Distributions 27. Assume a binomial probability distribution has p = .60 and n = 200, What are the mean and standard deviation? Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. What is the probability of 100 to 110 successes? What is the probability of 130 or more successes? What is the advantage of using the normal probability distribution to approximate the binomial probabilities? Use part (d) to explain the advantage.Question 3 Consider a binomial distribution with a success probability of p = 0.65 and repeated 100 timea. What is the normal distribution that approximates this binomial distribution? Use the approximation to find the probability that the number of successes is between 60 and 70 in the 100 repetitiona. Next consider the same binomial distribution except that it is repeated 1, 000 times. What is the normal distribution that approximates this binomial distribution with 1, 000 repetitions? Use the approximation to find the probability that the number of successes is between 600 and 700 in the 1, 000 repetitions. Find & such that the probability of the number of successes between 650 - x and 650 + x in 1, 000 repetitions in the same as the probability of success between 60 and 70 in 100 repetitions. In STATA, perform the following: set oba 100 gen B100 = rbinomial(100,0.65) histogram B100 set oba 1000 gen B1000 = rbinomial (1000,0.65) histogram B1000 What do these commands do? Do the histograms illustrate the results above.#6. The shape of the graph of a binomial distribution depends on the value of both n and p. To see how the shape changes for a fixed value of n, you will let p vary and graph each probability distribution. Let X be a binomial random variable with n=20. a. For p=.12, .48, and .91, obtain the binomial probability distribution and a graph of each distribution. (Be sure to hand the graphs in with your assignment.) b. For small values of p, the binomial distribution is skewed to the For large values of p, the binomial distribution is skewed to the For values of p near 100 the binomial distribution is nearly symmetric.The Bank of America Trends in Consumer Mobility Report indicates that in a typical day. 51% of users of mobile phones use their phone at least once per hour, 26% use their phone a few times per day, 8% use their phone morning and evening, and 13% hardly ever use their phones. The remaining 2% indicated that they did not know how often they use their mobile phone (USA Today, July 7, 2014). Consider a sample of 150 mobile phone users. What is the probability that at least 70 use their phone at least once per hour? What is the probability that at least 75 but less than 80 use their phone at least on per hour? What is the probability that less than 5 of the 150 phone users do not know how oft they use their phone