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]
3 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]3 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
For what values of the variables are the following expressions defined? 5y+2
babymother [125]

Answer:

all possible y values

Step-by-step explanation:

5y + 2 is defined for all values of y.

3 0
3 years ago
Read 2 more answers
40 POINTS PLEASE HELP AND HURRY
pentagon [3]

Answer:

The histogram that represents the correct frequency of each class interval in the given data set, is: histogram B.

What is a Histogram?

A histogram is a type of bar graph that uses bins to represent the frequency of a class interval.

Given the data points above, the histogram in option B has the correct bars that represent the appropriate frequency of each class interval.

Therefore, the histogram that represents the data set given is Histogram B.

Learn more about histograms on:

brainly.com/question/18198700

Please Do this:

<h2><u><em>Please give me brainleist!</em></u></h2>

3 0
2 years ago
What is the range of the following list of numbers:
galina1969 [7]

Answer:

it would have a range of 6

Step-by-step explanation:

im guessing that u ment 4 and ten not 104 so ya

3 0
3 years ago
26
Fantom [35]
It’s 16 because you need to kiss the moon
3 0
3 years ago
Write the rule for finding the coordinates of a point’s 90⁰ clockwise rotation about the origin.
malfutka [58]
Unless told otherwise, the center ofrotation<span> is the </span>origin<span> (0, 0).</span>
8 0
3 years ago
Other questions:
  • The ratio of skiers to snowboarders is 1:2. There are 1250 more snowboarders than skiers. How many skiers and snowboarders are t
    5·1 answer
  • What is the slope of the line that goes through the points (-2,0) and (-2,5)
    11·2 answers
  • Please xplain if u answer
    6·1 answer
  • What shape best describes the cross section cut at an angle to the base of a right rectangular prism? I already tried rectangle
    13·2 answers
  • If x = 3 and y = 2, evaluate x^2y
    15·1 answer
  • HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    14·2 answers
  • How many ways can you write one whole as a fraction
    7·2 answers
  • Whoever guesses my favorite color first gets brainliest
    10·2 answers
  • Help I’ll give brainliest!
    13·2 answers
  • The morning temperature was at 23.5° F. Later that evening the temperature had dropped to 15.6° F. What was the change in temper
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!