1. Suppose you have a fair 6-sided die with the numbers 1 through 6 on the sides and a fair 5-sided die with the numbers 1 through 5 on the sides. What is the probability that a roll of the six-sided die will produce a value larger than the roll of the five-sided die? 2. What is the expected number of rolls until a fair five-sided die rolls a 3?

Answers

Answer 1

Answer:

Answer:

a. 0.5 or 50%

b. 5 rolls.

Step-by-step explanation:

a. There are 30 possible outcomes for this experiment, the sample space for the outcomes in which the six-sided die produces a value larger than the roll of the five-sided die is:

S={6,1; 6,2; 6,3; 6,4; 6,5; 5,1; 5,2; 5,3; 5,4; 4,1; 4,2; 4,3; 3,2; 3,1; 2,1}

There are five outcomes when rolling a 6, four when rolling a 5, three when rolling a 4, two when rolling a 3 and one when rolling a two.

The probability is:

$P = (5+4+3+2+1)/(5*6)=0.5$

b. The probability of rolling a 3 on the five-sided die is 1 in 5 or 0.20. The expected number of rolls until a fair five-sided die rolls a 3 is:

$E(x=1) = (1)/(p(x))=(1)/(0.2)= 5\ rolls$

Related Questions

An ordinary regression model that treats the response Y as normally distributed is a special case of a GLM, with normal random component and identity link function. 1. With a GLM. Y does not need to have a normal distribution and one can model a function of the mean of Y instead of just the mean itself, but In order to get the maximum likelihood estimates the variance of Y must be constant at all values of predictors. ii. The Pearson residual e_inty_i-muhatiysqrt(muhat_) for a GM has a large-sample standard normal distribution (a)) True False, (w) True; (b)) True 00 True True (co False 0 false, Oll) False; IdFalse 00 True (1) False;
To make the cone, melted chocolate is pumped onto a huge cold plate at a rate of 2 ft3/sec. Due to the low temperature, the chocolate forms the shape of a cone as it solidifies quickly. If the height is always equal to the diameter as the cone is formed, how fast is the height of the cone changing when it is 5 ft high?
The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides? Part B Explain how you know. Provide at least one reason for your answer.
What is the domain of the function?Question 2 options:all real numbers greater than or equal to 1all real numbers less than or equal to 5all real numbers less than or equal to 1all real numbers
A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this store in week t after its release is R=f(t)=350 ln tR=f(t)=350lnt with t>1. Find f(5), f'(5), and the relative rate of change f'/f at t=5. Interpret your answers in terms of revenue.

A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 students' scores on the exam after completing the course: 37,12,12,17,13,32,23 Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Step 1 of 4 : Calculate the sample mean for the given sample data. Round your answer to one decimal place.

Answers

Answer:

The 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).

Step-by-step explanation:

The net change in 7 students' scores on the exam after completing the course are:

S = {37 ,12 ,12 ,17 ,13 ,32 ,23}

Compute the sample mean and sample standard deviation as follows:

$\bar x=(1)/(n)\sum x=(1)/(7)* 146=20.857\n\ns=\sqrt{(1)/(n-1)\sum (x-\bar x)^(2)}}=\sqrt{(1)/(7)* 622.8571}=10.189$

As the population standard deviation is not known, a t-interval will be formed.

Compute the critical value of t for 80% confidence interval and 6 degrees of freedom as follows:

$t_(\alpha/2, (n-1))=t_(0.20/2, (7-1))=t_(0.10,6)=1.415$

*Use a t-table.

Compute the 80% confidence interval for the average net change in a student's score after completing the course as follows:

$CI=\bar x\pm t_(\alpha/2, (n-1))*(s)/(√(n))$

$=20.857\pm 1.415*(10.189)/(√(7))\n\n =20.857\pm 5.4493\n\n=(15.4077, 26.3063)\n\n\approx (15.4,26.3)$

Thus, the 80% confidence interval for the average net change in a student's score after completing the course is (15.4, 26.3).

The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?

Answers

Answer:

year 2139

Step-by-step explanation:

The population will double when the factor e^(.005t) is 2.

e^(.005t) = 2

.005t = ln(2)

t = ln(2)/0.005 = 138.6

The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.

The population will double by the year 2139 from its value of 2.6 million in year 2000.

Population function :

$P(t) = 2.6 {e}^(0.005t)$

Population size at t = 0

$P(0) = 2.6 {e}^(0.005(0)) = 2.6(1) = 2.6$

Population at t = 2.6 million.

For the population to double ;

2.6 × 2 = 5.2 million :

$5.2 = 2.6 {e}^(0.005t)$

We solve for t

$(5.2)/(2.6) = {e}^(0.005t)$

$2 = {e}^(0.005t)$

Take the In of both sides

$ln(2) = 0.005t$

$t \: = ln(2) / 0.005 = 138.629$

The population will double after 139 years

Therefore, the population will double by the 2139 (Year 2000 + 139 years) = year 2139.

Learn more : brainly.com/question/11672641?referrer=searchResults

Solve for e.
9e + 4 = -5e + 14 + 13e

Answers

Answer:

e = 10

Step-by-step explanation:

In this problem we are told to solve for e. This means we need to isolate the variable e, leaving it completely by itself on one side of the equation.

9e + 4 = -5e + 14 + 13e

We can do this multiple ways, but I will show you how I would do it.

First I would subtract 4 from both sides.

9e + 4 = -5e + 14 + 13e

9e = -5e + 14 + 13e - 4

We can simplify the right side of the equation down by subtracting four from 14.

9e = -5e + 10 + 13e

Next, let's simplify our algebraic expressions. We can subtract 5e from 13e (or add -5e to 13e whatever tickles your fancy)

-5e + 13e = 8e

9e = 8e + 10

Now we subtract algebraic expression 8e from both sides

9e - 8e = 10

All of our expressions with the variable e are now on one side but we aren't done yet. Compute 9e - 8e.

9e - 8e = 10

1e = 10

e = 10

We have isolated e! Our final answer is e = 10

A coin is tossed and a fourth section spinner is spun once a tree diagram shows the possible outcomes for the two events what is the probability of flipping tails on a coin and spinning a two on the spinner

Answers

Answer:

2/6 or 1/3 I think

Step-by-step explanation:

you have a 1 out of 2 chances to land tails and 1 out of 4 chance to role a 2 on the spinner. so in total there is 6 chances for rolling and flipping the coin. and there is only 1 chance for both in the odds.

therefore I believe that its is 1/3 or 2/6. I do not know if I am right exactly but that is my thought process.

C) Which of these numbers is a square number?
A B C D
4х 10 9x 10* 4x 10 9x 10

Answers

Answer:

could you put the choices in order for me to help you out please

Need answer to. Add 3x-3and4x^2-6x

Answers

3x-3+4x^2-6x
4x^2-6x+3x-3 (arrange them in order)
4x^2-3x-3

do u want more simplified form ?

Other Questions

Which statement is true.?

A cube has an edge of 3 feet. The edge is increasing at the rate of 4 feet per minute. Express the volumeof the cube as a function of m, the number of minutes elapsed.Hint: Remember that the volume of a cube is the cube (third power) of the length of a side.

What are the coordinates of the vertices of the polygon in the graph that are in Quadrant I? Question 7 options: A) (–3,–4) B) (1,1), (2,2), (2,5), (5,5) C) (2,–3), (3,–4), (5,–4) D) (–4,2), (–2,5)

Find the value of x that will make L||M