1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lynna [10]
2 years ago
9

A red die, a blue die, and a yellow die (all six sided) are rolled. we are interested in the probability that the number appeari

ng on the blue die is less than that appearing on the yellow die, which is less than that appearing on the red die. that is, with b, y, and r denoting, respectively, the number appearing on the blue, yellow, and red die, we are interested in p(b < y < r).
Mathematics
1 answer:
NISA [10]2 years ago
6 0

5/54 or approximately 0.092592593  
There are 6^3 = 216 possible outcomes of rolling these 3 dice. Let's count the number of possible rolls that meet the criteria b < y < r, manually.
 r = 1 or 2 is obviously impossible. So let's look at r = 3 through 6.
 r = 3, y = 2, b = 1 is the only possibility for r=3. So n = 1
 r = 4, y = 3, b = {1,2}, so n = 1 + 2 = 3
 r = 4, y = 2, b = 1, so n = 3 + 1 = 4
 r = 5, y = 4, b = {1,2,3}, so n = 4 + 3 = 7
 r = 5, y = 3, b = {1,2}, so n = 7 + 2 = 9
 r = 5, y = 2, b = 1, so n = 9 + 1 = 10
 
 And I see a pattern, for the most restrictive r, there is 1 possibility. For the next most restrictive, there's 2+1 = 3 possibilities. Then the next one is 3+2+1
= 6 possibilities. So for r = 6, there should be 4+3+2+1 = 10 possibilities.
Let's see
 r = 6, y = 5, b = {4,3,2,1}, so n = 10 + 4 = 14
 r = 6, y = 4, b = {3,2,1}, so n = 14 + 3 = 17
 r = 6, y = 3, b = {2,1}, so n = 17 + 2 = 19
 r = 6, y = 2, b = 1, so n = 19 + 1 = 20 
 And the pattern holds. So there are 20 possible rolls that meet the desired criteria out of 216 possible rolls. So 20/216 = 5/54.
You might be interested in
A average amount of money on deposit in a savings account is $7500. Suppose a random sample of 49 accounts shows the average in
Valentin [98]

Answer:  

z=-3.79

p_v =2*P(z  

Step-by-step explanation:  

1) Data given and notation  

\bar X=6850 represent the mean average amount of money on deposit in savings account for the sample  

\sigma=1200 represent the population standard deviation for the sample  

n=49 sample size  

\mu_o =7500 represent the value that we want to test

\alpha=0.01 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

2) State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean for the amount of money on deposit in savings account differs from 7500, the system of hypothesis would be:  

Null hypothesis:\mu =7500  

Alternative hypothesis:\mu \neq 7500  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

3) Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{6850-7500}{\frac{1200}{\sqrt{49}}}=-3.79  

4)P-value  

Since is a two-sided test the p value would be:  

p_v =2*P(z  

5) Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average amount of money deposit in savings account its significantly different from 7500 tons at 1% of signficance.  

7 0
3 years ago
Answer to be named brainliset get 25 pts and get a thank you
lisabon 2012 [21]

Answer:

The scale factor is .625 is false The scale factor 1.6 is true

Step-by-step explanation:

Since the triangle gets bigger the multiplication factor needs to be more than one to make the end result bigger

4 0
3 years ago
Which phrase describes an unknown or changeable quantity?
Flura [38]

Answer:

That is a variable.

Step-by-step explanation:

- opposed to a constant which is known and does not change.

3 0
1 year ago
Each year a scientist measures the water level of a local lake. Negative numbers indicate that the water level is below its hist
STatiana [176]

Answer:

A

Step-by-step explanation:

Because when a decimal is only one number after a zero, it equals ten of whatever number it is. Since 60 is greater than 41 it is -0.6 ( -0.60 ) has more negative value than -0.41.

5 0
3 years ago
If the point (−1,3) is translated according to the rule (x,y)→(x+4,y−2), and then reflected across the x-axis, what are the coor
Artemon [7]

Answer:

hi

Step-by-step explanation:

rfshs hmm jtutq JK jehewyywgu

5 0
2 years ago
Read 2 more answers
Other questions:
  • John borrows $6.50 from his friends to pay for snacks, and $11.75 from his sister to go to the movies how much money does he nee
    5·2 answers
  • 3(125-4)-18 i need help
    12·2 answers
  • Which is true about this division problem? Select all
    15·2 answers
  • Which point is not on the graph of the function y = x + 5?
    12·1 answer
  • Which statement is true about the ratios of squares to circles in the tables? O The ratios in Table A are greater than the ratio
    7·2 answers
  • The elivation of city A is 60 feet above sea level; the elevation of city C is 12 feet above sea level. The elevation of city D
    15·1 answer
  • Pelase answer the question in the picture
    10·1 answer
  • What is the solution to the inequality? <br> 5(x−2)&lt;−3x+6
    11·1 answer
  • Find the distance between each pair of points.
    7·1 answer
  • Explore the difference between volume and pitch as well as what causes them.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!