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
barxatty [35]
2 years ago
8

A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the

event that the sum of the numbers falling uppermost is 5. Determine whether Eand Fare independent events.Show your calculationsby describing the sample space, theeventsE and F, and combinations of these events as needed.
Mathematics
1 answer:
iris [78.8K]2 years ago
6 0

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

Event\ 1 = \{1,2,3,4,5,6\}

Next, we list out the sample space of F

Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\

6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}

In (1): the sample space of E is:

E = \{1\}

So:

P(E) = \frac{n(E)}{n(Event\ 1)}

P(E) = \frac{1}{6}

In (2): the sample space of F is:

F = \{5,5,5,5\}

So:

P(F) = \frac{n(F)}{n(Event\ 2)}

P(F) =\frac{4}{36}

P(F) =\frac{1}{9}

For E and F to be independent:

P(E\ and\ F) = P(E) * P(F)

Substitute values for P(E) and P(F)

This gives:

P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}

P(E\ and\ F) = \frac{1}{54}

However, the actual value of P(E and F) is 0.

This is so because E = \{1\} and F = \{5,5,5,5\} have 0 common elements:

So:

P(E\ and\ F) = 0

Compare P(E\ and\ F) = \frac{1}{54} and P(E\ and\ F) = 0.

These values are not equal.

Hence: the two events are not independent

You might be interested in
Solve the system of equations <br><br> 5x-7y=58<br> y=-x+2<br><br> What is y and x equal to
QveST [7]

Answer:

A) 5x-7y=58

B) y=-x+2  we rearrange B) into

B) x + y = 2  then we multiply B) by -5

B) -5x -5y = -10  adding this to A)

A) 5x -7y = 58  we get

-12y = 48

y = -4

B) x + y = 2

x = 2 +4

x = 6



Step-by-step explanation:


6 0
2 years ago
Please help me I have to turn in by 8:00
Diano4ka-milaya [45]

Answer:

A 2

Step-by-step explanation:

When we divide x by 9 there is some whole number we will call y plus a remainder of 4

x/9 = y  remainder 4

Writing this in fraction form

x/9 = y + 4/9

Multiplying each side by 9

9*x/9 = 9* y + 4/9 *9

x = 9y +4

Multiply each side by 2

2x = 2*(9y+4)

2x = 18y +8

Add 3 to each side

2x+3 = 18y +8+3

2x+3 = 18y +11

Divide each side by 9

(2x+3)/9 = 18y/9 +11/9

              = 2y + 9/9 +2/9

               =(2y+1 + 2/9)

  We know y is a whole number and 1 is a whole number so we can ignore 2y +1 when looking for a remainder)

2/9 is a fraction

Taking this back from fraction form to remainder from

                 (2y+1) remainder 2

7 0
2 years ago
Find f(x) and g(x) so that the function can be described as y = f(g(x)).<br><br> y = 4/x^2+9
dlinn [17]

I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,

One possible answer is f(x) = \frac{4}{x},  \ \ g(x) = x^2+9

Another possible answer is f(x) = \frac{4}{x+9}, \ \ g(x) = x^2

There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)

So in the first example above, we would have

f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.

Similar steps will happen with the second example as well (when g(x) = x^2)

4 0
3 years ago
G hiugw getwiuh gbrul giluhbgflkgfnj
algol13

Answer:

no

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Help! If anyone knows thanks
DerKrebs [107]
A:
2t
t is the number of toys

b:
(p+12)/16
p is the price
6 0
3 years ago
Read 2 more answers
Other questions:
  • Jack jumps 40 times per 4 minutes. How many times does he jump per 1 minute?
    8·1 answer
  • A bag contains 32 red​ blocks, 47 green​ blocks, 21 yellow​ blocks, and 25 purple blocks. You pick one block from the bag at ran
    5·1 answer
  • What temperature is ten degrees higher than minus seven?
    13·2 answers
  • What is the square root of 128r squared
    7·1 answer
  • Write expression using the distributive property to find the product of 9 x82
    10·1 answer
  • 2a+6a=-24<br>what is a? and how do I get the answer?
    5·1 answer
  • Sue mom asked for 50 dollars and she gave 18 cents how much more does she need to give her mom
    10·2 answers
  • Need help with this math ​
    11·1 answer
  • Somebody plz plz plz plz tell me how she got divided by 5!!! It’s URGENT
    5·1 answer
  • Triangles V U T, U T S, and T X R are connected. Sides V T, U T, T S, and T R are congruent. A farmer is building three triangul
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!