Three cards are drawn from a deck of 52 cards without replacement.

(a) What is the probability that the third card is a spade (♠) given that the first card is a spade?

(b) What is the probability that all cards are spades given that at least one of them is a spade?

(c) Let Y be the number of black cards drawn. What is the probability that all 3 cards are black given that the first card is a spade? An ace?

(d) Let X be the number of aces drawn. Find P[Y = 2|X = 2]

Three cards are drawn from a deck of 52 cards without replacement.

(a) What is the probability that the third card is a spade (♠) given that the first card is a spade?

(b) What is the probability that all cards are spades given that at least one of them is a spade?

(c) Let Y be the number of black cards drawn. What is the probability that all 3 cards are black given that the first card is a spade? An ace?

(d) Let X be the number of aces drawn. Find P[Y = 2|X = 2]

In the State of Texas, pickup trucks account for 23% of the State's registered vehicles. If 100 registered vehicles are selected at random, answer the following 5 questions:

1) What is the probability that exactly 10 of the selected vehicles are pickup trucks?

2) What is the probability that 20 or less of the selected vehicles are pickup trucks?

3) What is the probability that 30 or more of the selected vehicles are pickup trucks?

4) What is the expected number of pickup trucks?

5) If 1000 vehicles are selected at random, what is the expected number of pickup trucks?

Suppose that the probability that a certain machine will breakdown on any given day is 0.04, and let X denote the number of breakdowns that occur over the course of a year. (Assume it is not a leap year)

A. What is the expected number of breakdowns?

B. What is the variance?

C. What is the probability that the machine will have between 10 to 15 breakdowns a year?

D. Suppose a visiting technician wants to report on the effectiveness of the machine. Unfortunately, the technician can only observe the machine for a week. What is the probability that the machine will breakdown at least once during the technician’s visit?

USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five on parole who become repeat offenders. x 0 1 2 3 4 5 P(x) 0.227 0.387 0.226 0.122 0.037 0.001 (a) Find the probability that one or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .773 Correct: Your answer is correct. How does this number relate to the probability that none of the parolees will be repeat offenders? This is twice the probability of no repeat offenders. This is the complement of the probability of no repeat offenders. These probabilities are not related to each other. This is five times the probability of no repeat offenders. These probabilities are the same. Correct: Your answer is correct. (b) Find the probability that two or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .386 Correct: Your answer is correct. (c) Find the probability that four or more of the five parolees will be repeat offenders. (Round your answer to three decimal places.) .038 Correct: Your answer is correct. (d) Compute ?, the expected number of repeat offenders out of five. (Round your answer to three decimal places.) ? = 1.358 Correct: Your answer is correct. prisoners (e) Compute ?, the standard deviation of the number of repeat offenders out of five. (Round your answer to two decimal places.) ? = .76 Incorrect: Your answer is incorrect. prisoners

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X=6), n=10 , p=0.5

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X≤4), n=7, p=0.6

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

P(X=14), n=15, p=0.7

The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute.

(i) What is the probability of no views in a minute?

(ii) What is the probability of two or fewer views in 10 minutes?

(iii) What is the probability of two or fewer views in 2 hours?

Write a program that creates a two-dimensional array initialized with test data. Use any

primitive data type that you wish. The program should have the following methods:

• fillRandom. Accepts a reference to a two-dimensional array and fills it with random integers from 0 to 99
• formatPrint. This method should accept a two-dimensional array and print it out row by row
• getTotal. This method should accept a two-dimensional array as its argument and return the total of all the values in the array.
• getAverage. This method should accept a two-dimensional array as its argument and return the average of all the values in the array. Calls getTotal and getElementCount.
• getRowTotal. This method should accept a two-dimensional array as its first argument and an integer as its second argument. The second argument should be the sub- script of a row in the array. The method should return the total of the values in the specified row.
• getColumnTotal. This method should accept a two-dimensional array as its first argument and an integer as its second argument. The second argument should be the subscript of a column in the array. The method should return the total of the values in the specified column.
• getHighestInRow. This method should accept a two-dimensional array as its first argument and an integer as its second argument. The second argument should be the subscript of a row in the array. The method should return the highest value in the specified row of the array.
• getLowestInRow. This method should accept a two-dimensional array as its first argument and an integer as its second argument. The second argument should be the sub- script of a row in the array. The method should return the lowest value in the specified row of the array.
• getElementCount. This method should accept a two-dimensional array and returns the total number of elements in the array.

Demonstrate each of the methods in this program. Each (except for getElementCount, are called from main.

The main program will request the number of rows and columns as input, creates the two-dimensional array, and first calls fillRandom. A sample output is:

Please enter the number of rows and columns in a two dimensional array: 4 5

78 65 72 30 95

60 71 88 41 73

32 74 47 70 27

59 91 80 81 87

Output:
Processing the int array.

Total : 1321

Average : 66.05

Total of row 0 : 340

Highest in row 0 : 95

Lowest in row 0 : 30

Total of row 1 : 333

Highest in row 1 : 88

Lowest in row 1 : 41

Total of row 2 : 250

Highest in row 2 : 74

Lowest in row 2 : 27

Total of row 3 : 398

Highest in row 3 : 91

Lowest in row 3 : 59