MATHEMATICS COLLEGE

Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd}
B: {Sum of the numbers showing is 9,11, or 12}
Are events A and B independent? Why?

Answers

Answer 1
Answer:

Answer:

A and B are not independent.

Step-by-step explanation:

Two events are said to be independent if :P(A \cap B)=P(A)P(B)

A: {Sum of the numbers showing is odd}

B: {Sum of the numbers showing is 9,11, or 12}

Given two dice, the sample space is given as:

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

The outcomes of event A:{Sum of the numbers showing is odd}  are:

(2,1),  (4,1), (6,1),  (1,2), (3,2),(5,2), (2,3), (4,3), (6,3)

(1,4), (3,4),  (5,4),  (2,5),  (4,5),  (6,5), (1,6), (3,6),  (5,6)

P(A)=18/36

The outcomes of event B:{Sum of the numbers showing is 9,11, or 12} are:

(6,3), (5,4),(4,5) (6,5), (3,6), (5,6), (6,6)

P(B)=7/36

The intersection of A and B are:

(6,3), (5,4),(4,5) (6,5), (3,6), (5,6)

P(A\cap B)=6/36

We can see from the above that:

P(A)P(B)=(7)/(36)* (18)/(36)=(7)/(72)\neq P(A\cap B)

Therefore, events A and B are not independent.
Answer 2
Answer:

Final answer:

The events A and B are dependent because the outcome of one event affects the probability of the other event happening.

Explanation:

The events A and B are dependent because the outcome of one event affects the probability of the other event happening. To determine if two events are independent, we need to check if the probability of the intersection of A and B is equal to the product of their individual probabilities.



Let's calculate the probabilities:



  1. For event A, we need to find the sum of the numbers showing on the dice. In a fair die, there are 3 odd numbers (1, 3, and 5) out of 6 possible outcomes. So, the probability of event A is 3/6 or 1/2.
  2. For event B, we need to find the sum of the numbers showing on the dice. There are three possible sums that satisfy event B: 9 (3+6, 4+5, 5+4), 11 (5+6, 6+5), and 12 (6+6). Out of the 36 possible outcomes, there are 6 outcomes that satisfy event B. So, the probability of event B is 6/36 or 1/6.
  3. Now, let's check if events A and B are independent by calculating the probability of their intersection. The intersection of A and B is the event that both the sum is odd (event A) and the sum is 9, 11, or 12 (event B). There are no outcomes that satisfy both events A and B. So, the probability of the intersection is 0.
  4. Finally, let's check if the product of the individual probabilities is equal to the probability of the intersection. The product of the individual probabilities is (1/2) * (1/6) = 1/12, which is not equal to 0. Therefore, events A and B are dependent.



In summary, events A and B are dependent because the outcome of one event affects the probability of the other event happening.

Learn more about Probability here:

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Billy finished his history assignment in 1/4 hours. Then he completed he’s chemistry assignment in 1/3 hours. What’s the total amount of time bill spent doing these 2 assignments

Answers

Answer:

7/12 of an hour

Step-by-step explanation:

you add them, by finding the common denominator.

1/3=4/12

1/4=3/12

3/12+4/12=7/12

What is the y-intercept of y = -3x - 2​

Answers

This is written in slope-intercept form; y = mx + b

m = slope

b = y-intetcept

In the equation we are given;

m = -3

b = -2

Therefore, the y-intercept is -2

Best of Luck!

Answer:

-2

Step-by-step explanation:

y = mx + bis how slope intercept form is written. The "mx" is the slope while the "b" is the y-intercept. In the equation y = -3x -2, we can see that -2 is the y-intercept because it is the value of "b".

I’m very confused pls help 50 PTSFind the quadratic function y=ax^2 +bx+c whose graph passes through the given points. (-1,-11) (2,-26) (-3,-31)

Answers

The quadratic value function is y = -x² - 4x + 16

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

Let the function passes through the given points. (-1,-11) (2,-26) (-3,-31)

And , using the point (-1,-11) , we get

-11 = a(-1)² + b(-1) + c

-11 = a - b + c

Using the point (2,-26) , we get

-26 = a(2)² + b(2) + c

-26 = 4a + 2b + c

Using the point (-3,-31) , we get

-31 = a(-3)² + b(-3) + c

-31 = 9a - 3b + c

And , the three set of equations are

-11 = a - b + c

-26 = 4a + 2b + c

-31 = 9a - 3b + c

From the first equation, we can solve for c:

c = 11 - a + b

Substituting this expression for c into the other two equations, we get:

-26 = 4a + 2b + 11 - a + b

-31 = 9a - 3b + 11 - a + b

Simplifying these equations, we get:

-15 = 3a + 3b

-21 = 8a - 2b

Solving the first equation for b in terms of a, we get:

b = -5 - a

Substituting this expression for b into the second equation, we get:

-21 = 8a - 2(-5 - a)

Simplifying and solving for a, we get:

a = -1

Substituting this value of a into the equation for b that we found earlier, we get:

b = -5 - (-1) = -4

Finally, substituting these values of a and b into the equation for c that we found earlier, we get:

c = 11 - (-1) - (-4) = 16

Hence , the quadratic function that passes through the given points is given by y = -x² - 4x + 16

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Answers

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David is having a cookout. Hot dogs and buns are sold based on the following quantities per package.Item
Amount Per Package
Hot dog buns
12
Hot dogs
10
A
David thought that he would have to buy 12 packages of hot dog buns and 10 packages of hot dogs to have one bun for each hot dog.
What is the LEAST amount of each David would need to buy to have an equal number of hot dogs and buns?
David should buy 2 packages of buns and 2 packages of hot dogs,
David should buy 6 packages of buns and 5 packages of hot dogs.
с David should buy 5 packages of buns and 6 packages of hot dogs,
D David should buy 22 packages of buns and 22 packages of hot dogs
B

Answers

Answer:  Choice C)  David should buy 5 packages of buns and 6 packages of hot dogs.

========================================================

Explanation:

Focus on the hot dog buns for now

1 package = 12 hot dog buns

2 packages = 24 hot dog buns  (multiply both sides by 2)

3 packages = 36 hot dog buns (multiply original equation by 3)

We can see that the multiples of 12 are being listed. So we have

12, 24, 36, 48, 60, 72, 84, ...

as the possible number of hot dog buns we could get if we buy 1,2,3... packages.

The possible number of hot dogs we can get are

10, 20, 30, 40, 50, 60, 70, 80, ...

which are multiples of 10. Simply add 10 to each item to get the next one.

--------------------------------

Considering these two sets

12, 24, 36, 48, 60, 72, 84, ...

10, 20, 30, 40, 50, 60, 70, 80, ...

what is the lowest common multiple? That would be 60 since it is found in both lists and it is the smallest in common.

The LCM of 12 and 10 is 60.

If he wanted 60 hot dog buns, then 60/12 = 5 packages of buns is what he needs.

If he wanted 60 hot dogs, then he needs 60/10 = 6 packages of hot dogs.

Therefore, David should buy 5 packages of buns and 6 packages of hot dogs. The answer is choice C.

--------------------------------

Side note: a different way to find the LCM is to multiply 10 and 12 to get 10*12 = 120. Then we divide by the GCF 2 getting 120/2 = 60.

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B
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C
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D

x−4<−6
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100!!!! POINTS

Answers

Answer:

A x< of 6

Step-by-step explanation:
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