Ask question

Ask question

All categories

2 years ago

6

Mathew rolls a number cube labeled with the numbers 1−6. He then flips a fair coin. What is the probability that he rolls a 4 an

d flips a head?

2 answers:

KATRIN_1 [288]2 years ago

7 0

Answer:

0.083

Step-by-step explanation:

Numbers of Cube = 6

Faces on coins = 2

Therefore, The total outcomes = $6 \times 2 = 12$

Now the favourable outcome that he rolls a 4 & flips a head = 1

The probability that he rolls a 4 & flips a head = 1

$\frac{Favourable \: Outcome}{Total \: Outcome}$

=> The probability that he rolls a 4 & flips a head = $\frac{1}{2} = 0.83333/ approx. 0.83$

Therefore, The probability that he rolls a 4 & flips a head = 0.083

xxMikexx [17]2 years ago

6 0

Answer:

its 1/12

Step-by-step explanation:

just saw the question on edgen

You might be interested in

An arc on a circle measures 250°. Within which range is the radian measure of the central angle? 0 to StartFraction pi Over 2 En

Alex Ar [27]

Answer:

The central angle is within the range π to 3π/2

Step-by-step explanation:

To convert from degrees to radians, we multiply the angle in degrees by 180/π.

To convert from radians to degree, we multiply the angle in radians by 180°/π.

π/2 = π/2 X 180°/π= 90°

π rad = π X 180°/π= 180°

3π/2 = 3π/2 X 180°/π= 270°

2π = 2π X 180°/π= 360°

Therefore the angle 250 which is between 180 and 270 is within the range :

π to 3π/2

4 0

2 years ago

Read 2 more answers

Correct 89.6162 to two decimal places

JulsSmile [24]

Answer:

89.62

Step-by-step explanation:

Look at the 3rd place of decimals - this is 6 so we add one to the second place.

4 0

2 years ago

Read 2 more answers

Which model represents the factors of 4x2 – 9? An algebra tile configuration. 5 tiles are in the Factor 1 spot: 2 +x , 3 negativ

Arturiano [62]

Answer:

Step-by-step explanation:

4x² - 9

(2x)² - 3²

(2x + 3)(2x - 3)

Factor 1 spot:

2 tiles of x

3 tiles of positive 1

Factor 2 spot:

2 tiles of x

3 tiles of negative 1

5 0

2 years ago

Read 2 more answers

The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100,

Gre4nikov [31]

Answer:

A.the type 1 error probability is $\mathbf{\alpha = 0.0244 }$

B. β = 0.0122

C. β = 0.0000

Step-by-step explanation:

Given that:

Mean = 100

standard deviation = 2

sample size = 9

The null and the alternative hypothesis can be computed as follows:

$\mathtt{H_o: \mu = 100}$

$\mathtt{H_1: \mu \neq 100}$

A. If the acceptance region is defined as $98.5 < \overline x > 101.5$ , find the type I error probability $\alpha$ .

Assuming the critical region lies within $\overline x < 98.5$ or $\overline x > 101.5$ , for a type 1 error to take place, then the sample average x will be within the critical region when the true mean heat evolved is $\mu = 100$

∴

$\mathtt{\alpha = P( type \ 1 \ error ) = P( reject \ H_o)}$

$\mathtt{\alpha = P( \overline x < 98.5 ) + P( \overline x > 101.5 )}$

when $\mu = 100$

$\mathtt{\alpha = P \begin {pmatrix} \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline 98.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} + \begin {pmatrix}P(\dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{101.5 - 100}{\dfrac{2}{\sqrt{9}}} \end {pmatrix} }$

$\mathtt{\alpha = P ( Z < \dfrac{-1.5}{\dfrac{2}{3}} ) + P(Z > \dfrac{1.5}{\dfrac{2}{3}}) }$

$\mathtt{\alpha = P ( Z 2.25) }$

$\mathtt{\alpha = P ( Z$

From the standard normal distribution tables

$\mathtt{\alpha = 0.0122+( 1- 0.9878) })$

$\mathtt{\alpha = 0.0122+( 0.0122) })$

$\mathbf{\alpha = 0.0244 }$

Thus, the type 1 error probability is $\mathbf{\alpha = 0.0244 }$

B. Find beta for the case where the true mean heat evolved is 103.

The probability of type II error is represented by β. Type II error implies that we fail to reject null hypothesis $\mathtt{H_o}$

Thus;

β = P( type II error) - P( fail to reject $\mathtt{H_o}$ )

∴

$\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }$

Given that $\mu = 103$

$\mathtt{\beta = P( \dfrac{98.5 -103}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-103}{\dfrac{2}{\sqrt{9}}}) }$

$\mathtt{\beta = P( \dfrac{-4.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-1.5}{\dfrac{2}{3}}) }$

$\mathtt{\beta = P(-6.75 \leq Z \leq -2.25) }$

$\mathtt{\beta = P(z< -2.25) - P(z < -6.75 )}$

From standard normal distribution table

β = 0.0122 - 0.0000

β = 0.0122

C. Find beta for the case where the true mean heat evolved is 105. This value of beta is smaller than the one found in part (b) above. Why?

$\mathtt{\beta = P(98.5 \leq \overline x \leq 101.5) }$

Given that $\mu = 105$

$\mathtt{\beta = P( \dfrac{98.5 -105}{\dfrac{2}{\sqrt{9}}} \leq \dfrac{\overline X - \mu}{\dfrac{\sigma}{n}} \leq \dfrac{101.5-105}{\dfrac{2}{\sqrt{9}}}) }$

$\mathtt{\beta = P( \dfrac{-6.5}{\dfrac{2}{3}} \leq Z \leq \dfrac{-3.5}{\dfrac{2}{3}}) }$

$\mathtt{\beta = P(-9.75 \leq Z \leq -5.25) }$

$\mathtt{\beta = P(z< -5.25) - P(z < -9.75 )}$

From standard normal distribution table

β = 0.0000 - 0.0000

β = 0.0000

The reason why the value of beta is smaller here is that since the difference between the value for the true mean and the hypothesized value increases, the probability of type II error decreases.

8 0

2 years ago

The picture shows a person taking a pinhole photograph of himself. Light entering the opening reflects his image on the wall, fo

Yuki888 [10]

Since the triangle formed is similar, then the ratio of the triangle height(horizontal distance) and the base of the triangle(the person and image height) will be same. The calculation would be:

a/b= c/d
16in / (4ft + 8in)= c/ (5ft + 3in)
16in/(48in + 8in)= c/ (60in + 3 in)
16in/64in= c/63in
c=1/4 * 63 in= 15.75 in= 16inch

6 0

2 years ago

Read 2 more answers