All categories

2 years ago

B A pair of fair dice is rolled, If the sum of the spots is 7, determine the probability that one di showed a 2.

Mathematics

1 answer:

finlep [7]2 years ago

8 0

Answer:

$\text{Probability}=\frac{1}{3}$

Step-by-step explanation:

Given : A pair of fair dice is rolled, If the sum of the spots is 7.

To find : Determine the probability that one die showed a 2 ?

Solution :

A pair of fair dice is rolled the outcomes are,

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

The sum of the spots is 7 i.e. (4,3),(2,5),(5,2),(3,4),(1,6),(6,1).

Total possibility = 6

Favorable outcome is that one die showed a 2 i.e. (2,5),(5,2)= 2

The probability that one die showed a 2 is given by,

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}$

$\text{Probability}=\frac{2}{6}$

$\text{Probability}=\frac{1}{3}$

You might be interested in

Fourteen is 6 less a number (n). Which equation shows this relationship?

Klio2033 [76]

Answer:

14+6=n=20

Step-by-step explanation:n=20

8 0

3 years ago

Read 2 more answers

A random sample of 40 binomial trials resulted in 14 successes. test the claim that the population proportion of successes does

mylen [45]

Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

<h3>What are the hypotheses tested?</h3>

At the null hypotheses, we test if the proportion of successes equals 0.5, hence:

$H_0: p = 0.5$

At the alternative hypotheses, we test if it does not equal, hence:

$H_1: p \neq 0.5$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are given by:

$n = 40, \overline{p} = \frac{14}{40} = 0.35, p = 0.5$

Hence the test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

z = (0.35 - 0.5)/(0.5/sqrt(40))

z = -1.9.

<h3>What is the decision?</h3>

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.

Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ4

5 0

1 year ago

A polynomial that can be factored is called

Bingel [31]

<span>reducible.

hope this helps</span>

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%7B%7D%5E%7B2%7D%20-%204%20%7D%7B%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20-%206x%2

Nimfa-mama [501]

First of all, we can observe that