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
coldgirl [10]
3 years ago
12

An experiment consist of rolling 3 fair dice (1 red die, a blue die, and a white die) and recording the number rolled on each di

e. Assume that the dice are fair, so that all outcomes are equally likely.
1. What probability should be assigned to each outcome?
2. What is the probability that the sum of the numbers rolled is 6?
3. What is the probability that the sum of the numbers rolled is at most 5?
Mathematics
1 answer:
Setler79 [48]3 years ago
3 0
In 1, t<span>here are 6 outcomes for each die, so for three dice, the total combination is 6 x 6 x 6 = 216 outcomes. Hence, t</span><span>he probability of any individual outcome is 1/216 </span>

The outcomes that will add up to 6 are 
<span>1+1+4 </span>
<span>1+4+1 </span>
<span>4+1+1 </span>
<span>1+2+3 </span>
<span>1+3+2 </span>
<span>2+1+3 </span>
<span>2+3+1 </span>
<span>3+1+2 </span>
<span>3+2+1 </span>
<span>2+2+2 </span>

<span>Hence the probability is </span><span>10/216 </span>

In 3, the minimum sum of the three dice is 3. so we start with this 
<span>P(n = 3) </span>
<span>1+1+1 ; </span><span>1/216 </span>

<span>P(n = 4) </span>
<span>1+1+2 </span>
<span>1+2+1 </span>
<span>2+1+1 ; </span><span>3/216 </span>

<span>P(n = 5) </span>
<span>1+1+3 </span>
<span>1+3+1 </span>
<span>3+1+1 </span>
<span>1+2+2 </span>
<span>2+1+2 </span>
<span>2+2+1; </span><span>6/216 

The sum in 3 is 10/216 or 5/108</span>
You might be interested in
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product o
Keith_Richards [23]

Answer:

  32.1 g

Step-by-step explanation:

In each 3 grams of C, there are 2 grams of A and 1 gram of B. So, for some amount C, the amount remaining of A is 40 -(2C/3), and the amount remaining of B is (50 -C/3). Since the reaction rate is proportional to the product of these amounts, we have ...

  C' = k(40 -2C/3)(50 -C/3) = (2k/9)(60 -C)(150 -C) . . . for some constant k

This is separable differential equation with a solution of the form ...

  ln((150 -C)/(60 -C)) = at + b

We know that C(0) = 0, so b=ln(150/60) = ln(2.5). And we know that C(10) = 20, so ln(130/40) = 10a +ln(2.5) ⇒ a = ln(1.3)/10

Then our equation for C is ...

  ln((150 -C)/(60 -C)) = t·ln(1.3)/10 +ln(2.5)

__

For t=20, this is ...

  ln((150 -C)/(60 -C)) = 2ln(1.3) +ln(2.5) = ln(2.5·1.3²) = ln(4.225)

Taking antilogs, we have ...

  (150 -C)/(60 -C) = 4.225

  1 +90/(60 -C) = 4.225

  C = 60 -90/3.225 ≈ 32.093 . . . . . grams of product in 20 minutes

In 20 minutes, about 32.1 grams of C are formed.

7 0
2 years ago
Your class has 30 students. if 1/3 of them walk to school, how many students in your class walk to school
Delvig [45]
1/3 of 30 would be 10. So 10 students walk to school.
4 0
3 years ago
Which of the following is the product of the rational expression shown below? 5/2x-1 x 6/x
Rina8888 [55]

Answer:

30/(2x^2-x)

Step-by-step explanation:

5/(2x-1) * 6/x

Multiply the numerators

5*6 = 30

Multiply the denominatos

(2x-1) *x = 2x^2 -x


5/(2x-1) * 6/x = 30/x(2x-1) = 30/(2x^2-x)

4 0
3 years ago
Read 2 more answers
What does x equal to
hodyreva [135]

Answer:

i got 16.25=2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find points of discontinuity y=x^2+5x+6/x^2-16
taurus [48]

Answer:

  x=4 and x=-4

Step-by-step explanation:

We assume you intend ...

  y = (x^2 +5x +6)/(x^2 -16)

There will generally be points of discontinuity where the denominator is zero. Sometimes a denominator factor will be cancelled by a numerator factor, but the "hole" remains and there is still a discontinuity there.

Here, the denominator factors as the difference of squares:

  x^2 -16 = (x -4)(x +4)

There will be discontinuities where these factors are zero, at x=4 and x=-4.

6 0
3 years ago
Other questions:
  • While taking inventory at her bakery, Ruby noticed that she had 5⁄6 pound of cinnamon yesterday, but now had only 2⁄3 pound. How
    10·1 answer
  • Change 4 5/7 and 7 into improper fractions
    6·1 answer
  • In Hamilton County, Ohio the mean number of days needed to sell a home is days (Cincinnati Multiple Listing Service, April, 2012
    13·1 answer
  • Mean:<br>median:<br>mode:<br>plz help
    8·2 answers
  • The Hu family goes out for lunch, and the price of the meal is $43. The sales tax on the meal is 7%, and the family also leaves
    15·1 answer
  • Let P(n) be the statement that n! &lt; nn where n is an integer greater than 1.
    5·1 answer
  • How to solve 17=-13-8x
    6·2 answers
  • Y/-5=1/10<br> Enter your answer as a reduced fraction.
    8·1 answer
  • Choose the graph of y = –3x – 1
    6·2 answers
  • A right prism has a triangular base. The length of the base is 6 meters and the height of the base is 4 meters. The height of th
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!