MATHEMATICS MIDDLE SCHOOL

Manuel rolls a fair pair of six-sided dice. The sample space of all possible outcomes is shown below.Let A be the event that the first die is six and B be the event that the second die is four.
What is P(A or B), the probability that the first die is six or the second die is four?

Answers

Answer 1

Answer:

The formula for probability is given as:

Probability = Number of requiredevents / Totalnumber of outcomes.

P(A) = 6/36 = 1/6

P(B) = 6/36 = 1/6

P(A ∩ B) = 1/36

The probability that the firstdie is six or the seconddie is four.

= P(A U B)

= P(A) + P(B) - P(A ∩ B)

The probability that the firstdie is six or the seconddie is four is 11/36 .

What is probability?

It is the chance of an event to occur from a totalnumber of outcomes.

The formula for probability is given as:

Probability = Number of requiredevents / Totalnumber of outcomes.

We have,

The number of possibleoutcomes in the samplespace of rolling two dice.

n(S) = 6 x 6 = 36

A = event that the firstdie is a six.

A = { (6,1), (6,2), (6, 3), (6, 4), (6, 5), (6, 6) }

n(A) = 6

B = event that the seconddie is a four.

B = { (1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4) }

n(B) = 6

Now,
P(A) = 6/36 = 1/6

P(B) = 6/36 = 1/6

P(A ∩ B) = 1/36

Now,

The probability that the firstdie is six or the seconddie is four.

= P(A U B)

= P(A) + P(B) - P(A ∩ B)

= 1/6 + 1/6 - 1/36

= 2/6 - 1/36

= (12 - 1)/36

= 11/36

Thus,

The probability that the firstdie is six or the seconddie is four is 11/36.

Learn more about probability here:

brainly.com/question/14099682

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Answer 2

Answer:

11/36

Step-by-step explanation:

First die 6: 6 possibilities

Second die 4: 6 possibilities

Intersection: 1 possibility (6,4)

P(A or B) = (6 + 6 - 1)/36

11/36

Related Questions

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which is a good comparison of the estimated sum and the actual sum of 7 10/12+2 11/12? Greater or lesser
there are four Defenders on a soccer team that this represents 20% of the players on the team which equation can be used to find the total players on the team plzz help me like this is hard
Just rationalize and simplify
Simplest form of 4/8

Given: F(x) = x + 2 and G(x) = 3x + 5(F - G) (x) =

1) 4
2) -3x - 3
3) -2x - 3

Answers

the answer will be 3) if not search or wait for multiple answers and pick the best choice

Suppose Y varies directly as X, and y = 9 when x = 3/2. Find y when x = 1.

Answers

Answer: The required value of y is 6.

Step-by-step explanation: We are given that y varies directly as x and y = 9 when $x=(3)/(2).$

We are to find the value of y when x = 1.

According to the given information, we have

$y\propto x\n\n\Rightarrow y=k* x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{where k is the constant of integration}]\n\n\Rightarrow y=kx~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

When y = 9 and $x=(3)/(2),$ we have from equation (i) that

$9=k*(3)/(2)\n\n\n\Rightarrow k=(18)/(3)\n\n\Rightarrow k=6.$

So, equation (i) becomes

$y=6x.$

Therefore, when x = 1, we get

$y=6*1=6.$

Thus, the required value of y is 6.

to vary directly is to be in proportion

y/x = y/x

9/(3/2) = y
9(2/3) = y
y = 6

Students in Miss Moseley's fourth grade class are learning multiplication, and they demonstrate mastery by passing assessments. Travis has passed 11 tests, and his classmate, Jenifer, has passed 2 tests. Going forward, Travis plans to pass 2 tests per week. Meanwhile, Jenifer plans to pass 5 tests per week. Eventually Jenifer will catch up to Travis. When the number of tests each student has passed are equal, how many tests will each student have passed and how many weeks will it take?

Answers

Answer:
Each will have passed 17 tests and it will take 3 weeks.

Explanation:
Let x be the number of weeks.
The number of tests Travis passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.

The number of tests Jenifer has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.

Setting these equal, we have:
11+2x=2+5x.

Subtract 2x from each side:
11+2x-2x=2+5x-2x;
11=2+3x.

Subtract 2 from each side:
11-2=2+3x-2;
9=3x.

Divide both sides by 3:
$(9)/(3) = (3x)/(3)$ ;
3=x.

It will take 3 weeks.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.

Answer:

Each will pass 17 test after 3 weeks.

Step-by-step explanation:

Consider the provided information,

Let x is the number of weeks.

Travis has passed 11 tests and plans to pass 2 tests per week.

$11+2x$

Jenifer, has passed 2 tests and plans to pass 5 tests per week.

$2+5x$

Now equate them as shown.

$11+2x=2+5x$

$11-2=5x-2x$

$9=3x$

$x=3$

Hence, after 3 weeks both have passed the same number of test.

Substitute x=3 in $11+2x$

$11+2(3)=17$

Hence, each will pass 17 test after 3 weeks.

Start time: 2:00 pm
elapsed time:_________ end time 8:30 pm

Answers

Start time: 2:00 pm
Elapsed time: 6 hours and 30 minutes.
End time 8:30 pm

Well, they begin at 2pm and end at 8:30
Subtract 2 hours from 8:30 6:30

Elapsed Time: 6 Hours 30 Minutes

There are 3,072 books in the school library. There are 96 sixth graders. If the sixth graders teamed up to read all the books, how many books would each sixth grader need to read

Answers

The only thing you should do is to divide 3,072 by 96 and the answer is 32.
So each of them should read 32 books :)))
I hope this is helpful
have a nice day

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