“Please answer all the questions and provide rationale for the answer for each question using your own words and show your calculations to get full credit”. 1. Which of...

An urn contains 4 white and 4 black balls. We randomly choose 4 balls. If 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again...

Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the teams is stronger than the other and wins each...

Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. If Smith always bets that the outcome will be one of the numbers 1 through 12, what is the...

If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1/100, what is the (approximate) probability that you will win a prize (a) at...

The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probability that there will be (a) at least 2 such accidents in the next...

The expected number of typographical errors on a page of a certain magazine is .2. What is the probability that the next page you read contains (a) 0 and (b) 2 or more...

It is known that diskettes produced by a certain company will be defective with probability .01, independently of each other. The company sells the diskettes in packages of...

A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day each of the components...

A communications channel transmits the digits 0 and 1. However, due to static, the digit transmitted is incorrectly received with probability .2. Suppose that we want to...

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct....

In Exercises 19–22, find the area of the parallelogram whose vertices are listed. (0,-2),(5,-2),(-3,1),(2,1)

Let A and P be square matrices, with P invertible. Show that $\text{det}(PAP^{-1})=\text{det }A$

In Exercises 24–26, use determinants to decide if the set of vectors is linearly independent $$\begin{bmatrix} 4 \\\\ 6 \\\\ 2 \end{bmatrix}, \begin{bmatrix} -7 \\\\ 0... 1 answers and 2 views Asked by 18 days ago In Exercises 21–23, use determinants to find out if the matrix is invertible.$$ \begin{vmatrix} 5 & 1 & -1 \\\\ 1 & -3 & -2 \\\\ 0 & 5 & 3 ...

Find the determinants in Exercises 5–10 by row reduction to echelon form. \begin{vmatrix} 1 & 3 & 2 & -4 \\\\ 0 & 1 & 2 & -5 \\\\ 2 & 7 & 6 & -3 ...

In Exercises 39 and 40, A is an $n \times n$ matrix. Mark each statement True or False. Justify each answer. a. The cofactor expansion of det *A* down a column is equal to...

Add the downward diagonal products and subtract the upward products. Use this method to compute the determinants in Exercises 15–18.**Warning:** *This trick does not...