There are 5 pens in a container on your desk. Among them, 3 will write well but 2 have defective ink cartridges. You will select 2 pens (without replacement) to take to a business appointment. Select the most appropriate statement for each part (a-e) when considering calculating the probability that both pens are defective. a. Let X: the number of defective pens selected. X is a random variable. [Select ]
b. For each pen chosen from the container, we can consider "Defective" as the success and "Working" as the failure since we are interested in both pens being defective. [ Select] -
c. X is well approximated by a Binomial Random Variable X-Bin(n=2. pi=2/5) True
d. If the first pen was replaced before the second pen was selected (sampling with replacement), then X would be very well approximated by a Binomial Random Variable X-Bin(n=2, pi=2/5) True
e. Had you been drawing 2 pens (without replacement) from a container of 25 pens, X would be better approximated by a Binomial Random Variable.

Kindly check explanation

Step-by-step explanation:

Total Number of pens = 5

Number of defective pens = 2

Number of non-defective pens = 3

A.) number of defective pens selected :

X : {0, 1, 2}

It is possible that no defective pen will be selected ; 1 defective will be chosen or both pens are defective.

2.)

Defective as Success (since selecting a defective pen is the point of interest.

3.)

Since selection is done without replacement

Probability of success per selection is different for each selection ;

Number of defective = 2

Number of observations = 5

P(success on first selection) = 2/5

P(success on second selection) = 1/4

Hence, X is not well approximated by a binomial random variable.

4.) if selection is done with replacement ; then then the probability of success per selection will be the Same for each selection made. Hence, X will be well approximated by a binomial Random variable.

5.) If sampling is done without replacement, then the the hypergeometric function will be a more effective approximation.

answer: 19 is   2

step-by-step explanation: i just looked at your answer and wrote it down

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0