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
aleksklad [387]
3 years ago
5

Alice and Bob each choose at random a number between zero and two. We assume a uniform probability law under which the probabili

ty of an event is proportional to its area. Consider the following events:
A: The magnitude of the difference of the two numbers is greater than 1/3.
B: At least one of the numbers is greater than 1/3.
C: The two numbers are equal.
D: Alice's number is greater than 1/3.

Find the probabilities P(A), P(B), P(C) and P(D).
Mathematics
1 answer:
Mnenie [13.5K]3 years ago
8 0

Answer / Step-by-step explanation:

Before we start to answer this question, it would be nice to understand some basic definition and principles:

Random: This refers to an unpredictable pattern of arrangement.  Without a specific aim or logical procedural pattern.

Uniform Probability distribution: This is a type of probability distribution in which the outcomes of distribution irrespective of the pattern or distance results in equally likely outcomes.

Uniform distribution is one of the widely used distributions although it's one of the simplest ones. The idea behind this distribution is that, unlike the other distributions, the likelihood of the any outcome in the distribution range is the same.

Now that we have a brief knowledge of the key terms within the question, hence, to start answering the question,

(a) Starting with 0 for Alice, Bob can choose any number starting from   1 /  3 . As Alice increases, Bob has to increase his starting point as well. Therefore, after Alice passes  1 /  3 , Bob can start choosing numbers from 0. This creates 2 triangles with sides  1  / 3 . The area of them gives us the probability.

Therefore, : P = 2 ( 1/3 1/3 1/3)

                        = 4/9

(b) We can find the probability of having both the numbers less than  1  / 3 . Then we subtract this probability from 1.

We have: P = 1 - 1/3 . 1/3

                     = 8/9

(c) This is basically impossible as the area of a dot is negligible.

(d) It means that Alice needs to select a number between  1  / 3  and 1.

Therefore: P = 1 - 1 /3

                    = 2 / 3

You might be interested in
Hence, or otherwise, simplify fully (x² + 4) - (x - 2)2
raketka [301]

Answer:

fully simplified answer: x^2-2x+8

Step-by-step explanation:

6 0
3 years ago
Determine the slope and y intercept of the graph of the equation.
iren [92.7K]
1. Slope = -7
Y intercept= 8
7 0
2 years ago
Someone help factor. This for me
Ksenya-84 [330]

Answer:

w(4 - 11w)

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
What is the length of HG? What is the length of HI?
Dmitry_Shevchenko [17]
? + 8 = 11
Subtract 8 from both sides.
? = 3
HG = 8

? + 6 = 9
Subtract 6 from both sides.
? = 3
HI = 3
6 0
3 years ago
Read 2 more answers
The point given is on the terminal side of an angle theta. Find the exact values of the six trig functions of theta.. (-3,2)
Dima020 [189]
We can use SOH, CAH and TOA, but first we must find the length of a hypotenuse:
h =\sqrt{(-3) ^{2}+2^{2} } =  \sqrt{9+4}= \sqrt{13}
sin (theta)= 2/√13
cos ( theta) = -3/√13
tan (theta) = -2/3
cot (theta ) = -3/2
sec (theta) = 1/cos(theta ) = -√13/3
csc(theta ) = 1/ sin (theta) = √13/2 
7 0
3 years ago
Other questions:
  • Carpet, padding, and installation costs $23.23 per sq. yd. how much would it cost to carpet both bedrooms.
    7·1 answer
  • if a length of a rectangle is four times its width. what is its perimeter is 90m. how can I find the dimentions
    8·1 answer
  • Johnny Mac's sporting Goods bought a baseball glove from Rawlins sporting Goods for $66.00, They want to mark up the glove 70% o
    13·1 answer
  • I NEED HELP PLZ ASAP!!!!! In right triangle ABCD above, x = A. 6 B. 8 C. 6√2 D. 10 E. 13
    6·1 answer
  • You and your friend play a video game. You have a final score of 40 points, and your friend has a final score of -21 points. by
    6·2 answers
  • Help me find domain? Please
    13·1 answer
  • - LT2XO<br> 3) (5y2 – 2xy + 6x² – 3x + 7y - 9) + (3x² - 4x + 5) – (5y2 – 3y +6)
    8·1 answer
  • The diameter of a circle is 3.2 meters. Which is the circumference of the circle rounded to the nearest hundredth of a meter?
    9·1 answer
  • Based on a study, a theme park has reported that typical patrons were willing to pay
    11·1 answer
  • I will mark brainlist please help!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!