1. What is the sample space if you roll two dice? What is the probability of rolling a sum of 7?
2. You and a friend go to a restaurant where you both order a soup and a salad. There are four soups (A, B, C, D) and 3
salads (1, 2, 3) to choose from. If you and your friend decide to get completely unique meals, what is the sample space
of possible orders you can make?
3. Give 3 examples of disjoint events.
4. The probability that Bob gets to work on time is 80%. The probability that Sarah gets to work on time is 90%. The
probability that they're both on time is 72%. What's the probability that Bob OR Sarah is late for work?
5. Jake's Pizza Place is offering a deal where they'll deliver your pizza in under 30 minutes or your pizza is free. They
manage to deliver the pizza in under 30 minutes 92% of the time. What's the probability that you'll get your pizza for
free?
6. The probability that a randomly selected student in our class likes soccer is 54%. If we select 3 random students
from our class, what is the probability that all of them like soccer?
7. The probability that a randomly selected student in our class likes soccer is still 54%. If we select 4 random students
from our class, what is the probability that all of them don't like soccer?
8. There are 6 blue marbles, 5 red marbles, and 4 green marbles in a box. If you pull a green marble out of the box, what
is the probability that the next marble you draw is red?
9.60% of students in a class studied for a test AND got an A on that test. 75% of students studied for the test. What is
the probability that a student got an A given that they studied for the test?

Answers

Answer 1

Probabilities are used to determine how likely it is for an event to happen.

(1) A roll of two dice

Let the dice be A and B. The sample space of each is:

[tex]A = \{1,2,3,4,5,6\}\\B = \{1,2,3,4,5,6\}[/tex]

To get the sample space (S) of the sum of the dice, we simply add up the individual element of both dice. So, we have:

[tex]S = \{(1+1),(1+2),(1+3),(1+4),(1+5),(1+6),.............,(6+1),(6+2),(6+3),(6+4),(6+5),(6+6)\}[/tex]

This gives

[tex]S = \{2,3,4,5,6,7,.............,7,8,9,10,11,12\}[/tex]

The complete sample space is:

[tex]S = \{2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12\}[/tex]

[tex]n(S) = 36[/tex] --- the total outcomes

The probability of rolling a sum of 7 is:

[tex]P(7) = \frac{n(7)}{n(S)}[/tex]

Where

[tex]n(7) = 6[/tex] ---- number of 7's in the sample space

So, we have:

[tex]P(7) = \frac 6{36}[/tex]

[tex]P(7) = 0.167[/tex]

The probability of rolling a sum of 7 is 0.167

(2) Restaurant

We have:

[tex]Soup = \{A,B,C,D\}[/tex]

[tex]Salads = \{1,2,3\}[/tex]

To get the sample space (S), we simply pick the individual elements of the above data. So, we have:

[tex]S = \{A1, A2, A3,B1, B2, B3,C1, C2, C3,D1, D2, D3\}[/tex]

(3) Disjoint events

Events are said to be disjointed if they cannot happen at the same time. 3 examples are:

Event 1: You are in China. Event 2: You are in NigeriaEvent 1: Heading towards north. Event 2: Heading towards southEven 1: Outcome of even number in a roll of die. Event 2: Outcome of an odd number in the same die

(4) Bob and Sarah

Let

[tex]A \to[/tex] Bob gets to work on time

[tex]B \to[/tex] Sarah gets to work on time

[tex]P(A) = 80\% \\ P(B) = 90\%\\P(A\ n\ B) = 72\%[/tex]

The probability that Bob OR Sarah is late for work is represented as:

[tex]P(A'\ or\ B')[/tex]

This is calculated using:

[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]

Where:

[tex]P(A') = 1 - P(A) = 1 - 80\% = 20\%[/tex]

[tex]P(B') = 1 -P(B) = 1 - 90\% =10\%[/tex]

[tex]P(A\ n\ B') = P(A) \times P(B') = 20\% \times 10\% = 2\%[/tex]

So, we have:

[tex]P(A'\ or\ B') = P(A') + P(B') - P(A'\ n\ B')[/tex]

[tex]P(A'\ or\ B') = 20\% + 10\% - 2\%[/tex]

[tex]P(A'\ or\ B') = 28\%[/tex]

[tex]P(A'\ or\ B') = 0.28[/tex]

The probability that Bob OR Sarah is late for work is 0.28

(5) Jake's Pizza

Let

[tex]A \to[/tex] The proportion of time they deliver on time

[tex]B \to[/tex] You get your pizza for free

So:

[tex]P(A) = 92\%[/tex]

You get your pizza for free if they didn't deliver within 30 minutes.

This means that:

[tex]P(B) = 1 - P(A)[/tex] --- Complement rule

So, we have:

[tex]P(B) = 1 - 92\%[/tex]

[tex]P(B) = 0.08[/tex]

The probability that you get your pizza for free is 0.08.

(6) Students and Soccer

Let:

[tex]A \to[/tex] Probability that a student likes soccer

So:

[tex]P(A) = 54\%[/tex]

If all 3 selected students like soccer, the probability is calculated as:

[tex]Pr = P(A) \times P(A) \times P(A)[/tex]

[tex]Pr = P(A)^3[/tex]

[tex]Pr = 54\%^3[/tex]

[tex]Pr = 0.157[/tex]

The probability that all 3 selected students like soccer is 0.157

(7) Students and Soccer

Let:

[tex]A \to[/tex] Probability that a student likes soccer

[tex]B \to[/tex] Probability that a student does not like soccer

So:

[tex]P(A) = 54\%[/tex]

[tex]P(B)= 1 - P(A)= 1 - 54\% = 46\%[/tex] ---- Complement rule

If all 4 selected students do not like soccer, the probability is calculated as:

[tex]Pr = P(B) \times P(B) \times P(B) \times P(B)[/tex]

[tex]Pr = P(B)^4[/tex]

[tex]Pr = 46\%^4[/tex]

[tex]Pr = 0.045[/tex]

The probability that all 4 selected students do not like soccer is 0.045

(8) Marbles

[tex]Blue = 6 \\ Green = 4 \\ Red = 5[/tex]

When the green marble is selected, we are left with

[tex]Blue = 6 \\ Green = 3 \\ Red = 5[/tex]

The probability of selecting a red marble at this point is:

[tex]P(Red) = \frac{Red}{Blue + Green + Red}[/tex]

[tex]P(Red) = \frac{5}{6+3+5}[/tex]

[tex]P(Red) = \frac{5}{14}[/tex]

[tex]P(Red) = 0.357[/tex]

The probability that the next marble you draw is red is 0.357

(9) Studying for test

Let

[tex]A \to[/tex] Students got an A

[tex]B \to[/tex] Students studied for test

So:

[tex]P(A\ n\ B) = 60\% \\ P(B) = 75\%[/tex]

The probability that a student got an A given that they studied for the test is  represented as:

[tex]P(A | B)[/tex]

So, we have:

[tex]P(A | B) = \frac{P(A\ n\ B)}{P(B)}[/tex]

[tex]P(A | B) = \frac{60\%}{75\%}[/tex]

[tex]P(A | B) = 0.80[/tex]

The probability that a student got an A given that they studied for the test is  0.80

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Related Questions

The chord of a circle of radius 6 ft is 8 ft long . find the distance if the chord from the center.​

Answers

Referring to attached figure :

given values : -

radius of the circle = 6 ft

measure of chord = 8 ft (AB)

construction : -

I actually draw a perpendicular on chord from the centre, and we know that the perpendicular from centre on it bisects the given chord, therefore measure of

AC = BC = 1/2 × AB

AC = BC = 4 ft

now, let's apply Pythagoras theorem for triangle OCB,

we get :

OC² + CB² = OB²

OC² + 4² = 6²

OC² + 16 = 36

OC² = 36 - 16

OC² = 20

OC = [tex] \sqrt{20} [/tex] ft

OC = [tex] 2\sqrt{5} [/tex] ft

And here OC is the distance of chord from its center, therefore required answer is [tex] 2\sqrt{5} [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \: \: \: TeeNForeveR \: \: \: }}[/tex]

**PLEASE ANSWER THE QUESTION BELOW.**
WILL MARK BRAINLIEST IF YOUR ANSWER IS CORRECT, RELIABLE, AND GOOD. PLEASE ADD DECIMALS, THANK YOU!
Please look at the picture provided below.
NO LINKS OR FALSE ANSWERS.

Answers

Answer:

80.5 km/h

Step-by-step explanation:

divide the 426.65 by 5.3 hours to get 80.5/1 hr

Which of these is NOT a terminating decimal?
A) 1.88
B) 1.875
C) 0.88
D) 0.8

Answers

Answer:

D

Step-by-step explanation:

find
the selling
price
at the
cost price is
£1 200
and
you make
a
profit
26
[tex]\%[/tex]

Answers

Answer:

the selling price = 1512

Step-by-step explanation:

the profit = 1200 × 26/100

= 312

the selling price = profit + the cost

= 1200+ 312 = 1512

Can y’all help me with 17 and 18

Answers

Answer:

17 is 35 degrees and 18 is 43 degrees

Answer:

#17 is 35 degrees

#18 is 43 degrees

Step-by-step explanation:

#17.   90-55 = 35

#18.   90 - 47 = 43

Solve the problem, who ever will solve this will be marked as brainliest ​

Answers

Answer:

mark me as brainliest ❤️

Answer:

gain%=8%

hope it helps.stay safe healthy and happy...

The linear equation y = −5x − 18 is written in which form?

Answers

it’s written in slope intercept form .

Kyle has a total of 16 coins in his pocket. All the coins are nickels or quarters, and they have a total value of $2.20. How many nickels does Kyle have?
7 nickels
8 nickels
9 nickels
11 nickels

Answers

Answer:

9 nickels

Step-by-step explanation:

Answer:

9 nickels

Step-by-step explanation:

He doesn't have that many coins, and there are 4 choices, so let's use the guess method.

Try 7 nickels.

7 * $0.05 = $0.35

16 - 7 = 9

9 * $0.25 = $2.25

The quarters alone are worth more than $2.20, so this is not the answer. We need more nickels and fewer quarters.

Try 11 nickels.

11 * $0.05 = $0.55

16 - 11 = 5

5 * $0.25 = $1.25

$0.55 + $1.25 = $1.80

The coins are worth too little. We need fewer nickels and more quarters.

Try 9 nickels.

9 * $0.05 = $0.45

16 - 9 = 7

7 * $0.25 = $1.75

$0.45 + $1.75 = $2.20

The coins are worth the correct amount.

Answer: 9 nickels

A box had a volume of 456 cubic inches, with a length of 12 inches and a height of 4 inches l. Determine the width of the box.

Answers

The width is 9.5 inches

abc=1/2; b (;b= solve for b)

Answers

Answer:

[tex]abc - \frac{b}{2} = 0[/tex]

Can someone please help <3

Answers

Answer:

number (c)

Step-by-step explanation:

I am not sure about this

What would be the equation to you have a part time job. You work for 3h on Friday and 6h on Saturday. You also recieve an allowance of 20 per week. You earn 92 per week how much do you earn per hour at your part time job

What is the equation for this promblem?

Answers

Answer:

Step-by-step explanation:

So, to go about your question, we must first ask, how many hours a week is being worked?

In this problem, that is 9 hours per week.

Next, we must question how much per week is made

That is $92 per week

Finally, we must determine if the allowance is occuring many times in the week or just once.

In this problem, that is only occuring once for the week.

So, the equation we must setup is 9x +20 =92.

To solve the equation, we need to subtract 20 on both sides to isolate the variable, x.

9x+20=92

     -20     -20

Now our equation is

9x=72

Now, to finally get x by itself or to isolate x, you should divide 9 on both sides to cancel out the 9 being multiplied by the x.

9x=72

9     9

x=8 because of 72/9 is equal to 8.

I hope this helps, and I will answer any questions you have.

WILL GET MARKED THE BRAINIEST
Which logic statement represents this argument?

If it’s a weekend, I exercise. It’s not a weekend. So, I won’t exercise.

Assume that p represents “It’s a weekend” and q represents “I exercise.”

A.
(p q) p
B.
[(p q) p] q
C.
[(p q) p] q
D.
[(p q) p] q

Answers

Hey the signs are not showing if you write the signs I’ll answer it in the comments :))

A serving of walnuts is 1/2 of a cup. How many servings are there in a 1 1/2-cup bag of
walnuts?

Answers

Answer:

3

Step-by-step explanation:

1/2 a cup makes one serving in 1 1/2 a cup there are 3 servings

Please help probability

Answers

Answer:

3/11

There are 11 possibilities and only 3 are even and less than 7.

Help and hurry! Fastest and correct answer gets brainlesst.
No explanation needed
.
Here is a sketch of Noah's bedroom.
He wants to create a scale drawing of his bedroom to show to his designer.
He uses a scale of 1 m = 6 cm to draw his scale drawing.
He draws a 33 cm line to represent wall D.
What is the actual length of wall D according to the above mentioned scale?

Answers

Answer:

5.5 m

Step-by-step explanation:

1m = 6cm

x = 33 cm

x = 33 /6

= 5.5 m

A washer and a dryer cost $950 combined. The washer costs $ 100 more than the dryer. What is the cost of the dryer?

Answers

Answer:

$850

Step-by-step explanation:

washer + dryer = $950

if washer cost=>$100

Therefore; the value of the dryer should be x

$100+x=$950

x=$850

The dryer cost is =>$850

Answer:

The dryer is $425.

Step-by-step explanation:

Washer = 100 + Dryer

Set up an equation:

Variable x = dryer

x + x + 100 = 950

x + x = 850

2x = 850

x = 425

Dryer = 425

Bonus answer:

Washer = 100 + x

Washer = 100 + 425

Washer = 525

Check your work:

Washer + Dryer = 950

525 + 425 = 950

950 = 950

Correct!

Select the correct answer. Which statement best defines a circle?
A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center
B. the set of all points in a plane that are the same distance from a given point called the center
C. the set of all points that are the same distance from a given point called the center
D. points in a plane that surround a given point called the center

Answers

Answer:

A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center. hope this helps

Step-by-step explanation:

- Zombie

The statement best defines a circle is A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center.

What is a circle?

A circle is defined as a shape consisting of all points in a plane that are given the same distance from a given point called the center.

A circle can be characterized by its center's location and its radius's length.

The statement best defines a circle is A. the set of all points in a plane that are the same distance from each other surrounding a given point called the center.

Learn more about circle here:

https://brainly.com/question/10165274

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49q²-70q+25 resolve into fractors​

Answers

Answer:

(7q-5)²

Step-by-step explanation:

= 49q² - 70q + 25

= 49q² -35q -35q + 25

= 7q(7q-5) - 5(7q - 5)

= (7q-5) (7q-5)

= (7q-5)²

CMIIW

Answer:

Step-by-step explanation:

49q² -70q +25 , rewrite the first two terms as squares

(7q)² -70q + 5² , compare with  a² - 2ab + b² = (a-b)²

   

    a² - 2ab + b²

(7q)² -2(7q)(5 )+ 5², because 70q = 2*35q = 2*7*5*q

We can see that a = 7q and b=5, therefore

49q² -70q +25 = (7q -5)²

We set the equation equal to 0 to find the roots

7q-5 =0, add 5 to both sides

7q =5 , divide both sides by 7

q = 5/7 ≈ 0.714

A bag contains 8 black marbles, 5 white marbles and 12 red marbles. What is the probability of selecting a red marble, not replacing it, then selecting a white marble?

Answers

Answer:

1/10

Step-by-step explanation:

8 black marbles, 5 white marbles and 12 red marbles = 25 marbles

P(red) = red/total = 12/25

Remove the marble

8 black marbles, 5 white marbles and 11 red marbles = 24 marbles

P(white) = white/total = 5/24

P(red, remove,white) = 12/25 * 5/24

                                   =12/24 * 5/25

                                   =1/2 * 1/5

                                   =1/10

Step-by-step explanation:

Total balls = 12 + 5 + 8 = 25 marbles

Probability of getting white marbles = 5/24

Probability of red marbles = 12/24 = 1/2

Now

Probability = 1/2 × 5/24 + 1

Probability = 1/2 × 5/25

Probability = 5/50

Probability = ⅒

x/2 + 1 = 1/4x - 6 solve for x

Answers

x=-28......................

Is -15/6 a rational number?

Answers

yes, rational number means that it can be expressed as an fraction. -15/6 is a fraction, hence its a rational number

Answer:

Yes it is a rational number

Simplify negative 2 over 3 ÷ negative 7 over 4.

Answers

Answer:

[tex]-\frac{2}{3}/-\frac{7}{4}=\frac{8}{21}[/tex]

Step-by-step explanation:

Given: [tex]-\frac{2}{3}/-\frac{7}{4}[/tex]

Take the reciprocal of the divisor: [tex]-\frac{2}{3}/-\frac{4}{7}[/tex]

Multiply the two fractions instead: [tex]-\frac{2}{3}*-\frac{4}{7}[/tex]

Evaluate: [tex]\frac{8}{21}[/tex]

Answer:

8 / 21

Step-by-step explanation:

Find the x- and y-intercepts of the graph of — 2 + 3y = 37. State your answers as
whole numbers or as improper fractions in simplest form.

Answers

This will be true for all equations you ever come across.

x-intercepts are found by setting y=0 and solving for x.

y-intercepts are fond by setting x=0 and solving for y.

Equation: -x+3y=37

x-intercept: set y=0
Solve -x + 3(0) = 37 for x.

y-intercept: set x=0
Solve -(0) + 3y = 37 for y.
This one will have a fraction answer. Be sure to reduce the fraction.

solve the systems of linear equations using substitution
1.x-4y=-10 2.a-3b=24
2x+y=-11 a+2b=-16



3.4j-5k=27 4.m+n=-3
k=j-7 m-4n=27

Answers

Step-by-step explanation:

1 . x - 4y = -10

2x + y = -11

multiply the first equation with 2

2x - 8y = -20

-

2x + y = -11

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

= 0 - 9y = -9

y = 1

x = -6

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

2.

a - 3b = 24

-

a + 2b = -16

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

= 0- 5b = 40

b = - 8

a = 0

and so on

What's the volume of the following is rectangular prism plsssssss will mark brainlist HELPPPP

Answers

Answer: 6.75 or 6 3/4

Step-by-step explanation: 3 3/8 x 2 = 6.75 Brainliest please?

Write an exponential model given the two points (8,150) and (9,220).

Answers

Answer:

Step-by-step explanation:

The exponential model for the given points is y = 6.88(1.47)ˣ

What is exponential function?

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Given,

points are (8,150) and (9,220)

Exponential function,

y = abˣ            --------(A)

for point (8 , 150)

150 = ab⁸    -------(1)

for point (9 , 220)

220 = ab⁹    -------(2)

Dividing equation (2) by equation (1)

220/150 = ab⁹/ab⁸

Simplifying

1.47 = b

Substituting value of b in equation (1)

150 = a(1.47)⁸

150 = a(21.80)

a = 150/21.80

a = 6.88

Substituting value of a and b in equation(A)

y = 6.88(1.47)ˣ

Hence, y = 6.88(1.47)ˣ is the exponential model for given points.

Learn more about exponential function here:

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Write a rule in coordinate form for the translation from Triangle EFG to Triangle
E'F'G'.
(x,y)-->(x+2, y-1)
(x,y)-->(x+1, y-2)
(x,y)-->( X-2, y + 1)
(x,y)-->(x+3, y +2)

Answers

Answer:

1st option

Step-by-step explanation:

Consider the coordinates of F and F'

F (- 3, 4 ) and F' (- 1, 3 )

To go from - 3 → - 1 in the x- directions , means adding 2

To go from 4 → 3 in the y- direction means subtracting 1

Then translation rule is

(x, y ) → (x + 2, y - 1 )

28 points asap pls PLSSS

Answers

Answer:

Its answer is Commutative property

Step-by-step explanation:

Answer will be Commutative property

hope it helps

8x - 5y = 30 + 2x, for x

Answers

Answer:

[tex]8x - 5y = 30 + 2x \\ 8x - 2x = 30 + 5y \\ 6x = 30 + 5y \\ \\ x = \frac{30 + 5y}{6} \\ \\ x = \frac{30}{6} + \frac{5y}{6} \\ \\ x = 5 + \frac{5y}{6} [/tex]

I hope I helped you^_^

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