1. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy
in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball
for each question and replaces the ball in the box.


The marking on the ball will determine her answer
to the question. There are five multiple choice questions on the exam. What is the probability that she will get:

a. Five questions correct?

b. At least four questions correct?

c. No questions correct?

d. No more than two questions correct?

Answers

Answer 1

Answer:

a) 0.001 = 0.1% probability that she will get five questions correct.

b) 0.0156 = 1.56% probability that she will get at least four questions correct.

c) 0.2373 = 23.73% probability that she will get no questions correct.

d) 0.8965 = 89.65% probability that she will get no more than two questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she gets it correct, or she does not. The probability of getting a question correct is independent of any other question, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

There are five multiple choice questions on the exam.

This means that [tex]n = 5[/tex]

She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

a. Five questions correct?

This is [tex]P(X = 5)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001[/tex]

0.001 = 0.1% probability that she will get five questions correct.

b. At least four questions correct?

This is:

[tex]P(X \geq 4) = P(X = 4) + P(X = 5)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{5,4}.(0.25)^{4}.(0.75)^{1} = 0.0146[/tex]

[tex]P(X = 5) = C_{5,5}.(0.25)^{5}.(0.75)^{0} = 0.001[/tex]

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.001 = 0.0156[/tex]

0.0156 = 1.56% probability that she will get at least four questions correct.

c. No questions correct?

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]

0.2373 = 23.73% probability that she will get no questions correct.

d. No more than two questions correct?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]

[tex]P(X = 1) = C_{5,0}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]

[tex]P(X = 2) = C_{5,2}.(0.25)^{2}.(0.75)^{3} = 0.2637[/tex]

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965[/tex]

0.8965 = 89.65% probability that she will get no more than two questions correct.


Related Questions

What’s the answer?!!

Answers

Answer:

6x+10mm=p is the answer

brainlest plz

NO LINKS NO FILES. Write the next two integers: -48, -24, -12, _, _

Answers

Answer:

-6,-3

hope this helps

have a good day :)

Step-by-step explanation:

Which pair of expressions below are equivalent?

a. 7(2n) and 9
b. 3n + 5n and 15n
c. 4(2n-6) and 8n - 24
d. 7(2n) and 72n​

Answers

Answer:

The answer is C

Hope this helped!

Need help quick! Will give brainliest

Answers

The answer is A for sure

Why is it useful to factor out the GCF first when factoring?

Answers

it makes the problem simpler and earlier to solve

Answer:

Because it makes factoring easier because the coefficient are smaller requiring less step

Given the equation Y-4=3/4(x+8) in point-slope form, identify the equation of the same line in standard form

Answers

Answer:

3x-4y=-40

Step-by-step explanation:

Hi there!

We're given the equation of the line, y-4=3/4(x+8) in point-slope form (y-[tex]y_{1}[/tex]=m(x-[tex]x_{1}[/tex]), where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) is a point and m is the slope)

We need to convert y-4=3/4(x+8) into standard form (ax+by=c, where a, b, and c are integer coefficients; a CANNOT be 0, and CANNOT be negative).

So we need to get y-4=3/4(x+8) out of point-slope form

We can do this by converting the equation into slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

to do this, we need to isolate y by itself in the equation

first, do the distributive property and distribute 3/4 on the right side

y-4=3/4x+6

add 4 to both sides

y=3/4x+10

now the equation is in slope-intercept form, but remember, we want it in standard form

x and y are on the same side in standard form, so let's subtract 3/4 x from both sides

-3/4x+y=10

however we aren't done; in standard form, the coefficients need to be integers (whole numbers), and a (the coefficient in front of x) CANNOT be negative

so let's multiply both sides by -4 to clear the fraction and change the sign of a

-4(-3/4x+y)=-4(10)

do the distributive property

3x-4y=-40

Hope this helps! :)

WILL GIVE BRAINLIEST
4
3
2x + 4
x+7

Answers

Answer:

x = 8

Step-by-step explanation:

[tex]\frac{x+7}{3} =\frac{2x+4}{4}[/tex]

do cross multiplication

[tex]3(2x+4) = 4(x+7)\\6x + 12 = 4x + 28\\6x - 4x = 12 - 16\\2x = 16\\x = 16/2\\x = 8[/tex]

A children's inflatable pool takes 17 minutes to fill with an electric air pump. It takes 53 minutes to let the air out of the pool. If the pool's vale is accidentally left open, how long will ot take to fill the pool?

Answers

Answer:

less than 17 minutes

Step-by-step explanation:

ABCD is a quadrilateral such that the measures of three of its interior angles are given as B=122 degrees, C= 75 degrees, D= 51 degrees, find m=A

please help me with explanation ​

Answers

Answer:

angle A is 112 degree.

Step-by-step explanation:

quadilateral have 4 angles .

sum of the interior angles of a quadilateral is 360 degree

Here,

angle A = be x

angle B = 122

angle C = 75

angle D = 51

Now,

angle A + angle B + angle C + angle D =360 degree

x + 122 + 75 + 51 = 360

x + 248 = 360

x = 360 - 248

x = 112

170 lbs to kg round to nearest tenth​

Answers

Answer:

77.1 kg

Explanation:

NEED HELP ASAP!!! please!!


Is the graph of the function shown in the graph below one-to-one? why?

Answers

It’s not because if you draw a horizontal line it will pass through two points, if you draw a horizontal line and it only passes through one point then it’s a one to one function

this distance-time graph represents a journey made by Jo

Answers

a) At 10 minutes the line is at y - 1, which means she reached 1 km in 10 minutes.

b) The last 30 minutes would be 30 minutes to 60 minutes.

at 30 minutes she was at 0km at 60 minutes she was at 4 km, so in 30 minutes she traveled 4 km.  30 minutes is a half hour, so multiply distance by 2: 4 x 2 = 8, she was traveling at 8 km per hour.

need help very bad :((

Answers

Answer:

Step-by-step explanation:

First of all, I can't think of a single exception to this, but when you rotate a figure, the two figures are congruent If all you do is rotate it.

2y/2 = 5/2                Divide both sides by 2

y = 5/2

y = 2.5

2x = 67 degrees    Divide both sides by 2.

2x/2 = 67/2            x = 33.5

3w + 3 =12             Subtract 3 from both sides

3w + 3 -3 = 12-3    Combine

3w = 9                   Divide by 3

w = 9/3

w = 3

12(5x+10x^2)=480+60x




(^ = exponents)(show work)

Answers

x=−2 is the aswer to this problem i was wrong before

X=2 or X=-2 is the answer

Help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

9

Step-by-step explanation:

Length * Width = 43 * 36 = 1548 sq ft

1548 / 172 (sq ft per can of wood stain covered) = 9

Item 21
Subtract.

7,342−2,667

Answers

Answer:

4675

Step-by-step explanation:

The following data represent the number of loaves of bread, in thousands, which were sold by various grocery stores in the month of June. Construct a dot plot for the given data.

4, 8, 11, 10, 10, 4, 5, 13,
6, 13, 8, 14, 8, 1, 10, 9

Select any value to see the controls for increasing or decreasing the frequency.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Answers

Answer:

Following are the solution to these question:

Step-by-step explanation:

The frequency of the data value will be the same in dot plots for the number of dots. The frequency table is following:

[tex]X \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Frequency \\\\1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3\\\\11\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]

[tex]12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\\\\13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\\\\14\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1\\\\[/tex]

(05.01 MC) choose the systems of equations which matches the following graph​

Answers

Answer:

a

Step-by-step explanation:

x+2y=-10

-x       -x

2y=-10-x

y=(1/2)x-5

This is one of the lines and reduces the options to a or c.

3x-y=12

-3x    -3x

-y=12-3x

y=3x-12

This is the line with the positive slope and since both lines match, the answer is a.

A phone company offers two packages of service. Package A is $35.00 per month with an additional charge of $0.15 per minute for long distance. Package B is $50.00 per month with an additional charge of $0.10 per minute for long distance. How many minutes have to be used for the costs of both plans to be the same?

Answers

Answer:

at 300 minutes, the cost of both plans are equal

Step-by-step explanation:

Package A:  f(c) = 35 + .15c

Package B:  f(c) = 50 + .10c

to answer the question we can set both expressions equal to each other and solve for 'c'

35 + .15c = 50 + .10c

35 + .05c = 50

.05c = 15

c = 15/.05

c = 300

Classify each angle of the degrees

Answers

Answer:

acute

right angle or obtuse

obtuse

Step-by-step explanation:

those are the answers

A farmer needs to calculate the number of liters in 90 cubic meters of fertilizer. How many liters are equivalent to 90 cubic meters?

Answers

Answer:

Answer is 90,000

Step-by-step explanation:

Hope this helps!

What’s the value of X????

Answers

Answer:
137

Step-by-step explanation:

Sum of opposite angles in a quadrilateral embedded in a circle=180

43+x=180

X=180-43

X=137

A driver works 40 hours a week for the first two months on the job. How much more per week does the driver make after 28 days?

Answers

Answer:

is there something missing in this question. i cant understand

Step-by-step explanation:

please tell me if there is more to this

seven more than the quotient of a number and 2 is equal to 3 equation ​

Answers

Answer:

Step-by-step explanation:

seven more than the quotient of a number and 2 is 10

7+n/2=10 n=6 check 7+3=10 ok

Three airlines serve a small town in Ohio. Airline A has 48% of all scheduled flights, airline B has 26% and airline C has the remaining 26%. Their on-time rates are 81%, 61%, and 40%, respectively. A flight just left on-time. What is the probability that it was a flight of airline A?

Answers

Answer:

0.5969 = 59.69% probability that it was a flight of airline A

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Left on time.

Event B: From airline A.

Probability of a flight leaving on time:

81% of 48%(airline A).

61% of 26%(airline B)

40% of 26%(airline C). So

[tex]P(A) = 0.81*0.48 + 0.61*0.26 + 0.40*0.26 = 0.6514[/tex]

Probability of leaving on time and being from airline A:

81% of 48%. So

[tex]P(A \cap B) = 0.81*0.48 = 0.3888[/tex]

What is the probability that it was a flight of airline A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.3888}{0.6514} = 0.5969[/tex]

0.5969 = 59.69% probability that it was a flight of airline A

Laura, David, and Carlos served a total of 115 orders Monday at the school cafeteria. David served 3 times as many orders as Carlos. Laura served 10 more orders than Carlos. How many orders did they each serve?

Answers

Answer:

Step-by-step explanation:    ts  6  11    19    56

Laura, David, and Carlos served a total of 115 orders

David served 3 times as many orders as Carlos.                 David = 3x

Laura served 10 more orders than Carlos.                      let Carlos = x

How many orders did they each serve?                           Laura  =  x + 10

     Carlos  +  David  +  Laura  = 115

          x  +     3x    +    x+10       = 115

                        5x + 10     =  115

                               5x   =  115 - 10

                               5x   =  105

                                x   =   21    Carlos

                                          63   Davide

                                          31    Laura

                 add then up    115  Total

Assume X is normally distributed with a mean of 5 and a standard deviation of 2. Determine the value for x that solves each of the following.

a. P(X > x) = 0.5
b. P(X > x) = 0.95
c. P(x < X < 9) = 0.2
d. P(3 < X < x) = 0.95
e. P(-x < X - 5 < x) =0.99

Answers

Answer:

U = 5

S = 4

1.) P(X>x) = 0.5

Prob = 1-0.5 = 0.5

We have z = 0, that is the z score with the probability of 0.5

X = u + z(s)

= 5+0*4

= 5

2.) 1-0.95 = 0.05

Z score having this probability

Z = -1.64

X = 5-1.64*4

= 5-6.56

= -1.56

3.) P(z<1.0) - p(X<x) = 0.2

0.841345-0.2 = .641345

We find the z score given this probability

Z= 0.36

X = 5+0.36*4

= 5+1.44

= 6.44

4.) P(X<x)-P(Z<-.5)

0.95 = p(X<x)-0.308538

p(X<x) = 0.308538 + 0.95

= 1.258538

There is no x value here, given that the probability is more than 1.

5. 1-0.99/2 = 0.005

We get the z score value

= -2.58

U - 5 = 5-5 = 0

-x = 0-2.58(4)

X = 10.32

Balu had a collection of coins1/2 of the coins were from Asian countries,1/3

of them from European countries and the remaining 36 from America.

How many coins were from ASIAN countries?

A)18

B)30

C)108

D)216 step by step explanation please​

Answers

Step-by-step explanation:

[tex] \frac{1}{2} = asian \\ \frac{1}{3} = european \\ 36 = american \\ \frac{1}{2} + \frac{1}{3} = \frac{3 + 2}{6} = \frac{5}{6} \\ \frac{6}{6} - \frac{5}{6} = \frac{1}{6} = 36 \\ \frac{1}{6} = 36 \: so \\ \frac{6}{6} =6 \times 36 = 216 \\ \frac{1}{2} \times 216 = asian \\ \frac{1}{2} \times 216 = 108asian \\ please \: mark \: brainliest[/tex]

There are total 108 coins belonging to Asian countries.

What is equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Balu had a collection of coins 1/2 of the coins were from Asian countries, 1/3 of them from European countries and the remaining 36 from America.

Let the total number of coins be x,

Establishing the equation, we get,

x/3+x/2+36 = x

Multiplying the equation by 6, we get,

2x+3x+216 = 6x

6x-5x = 216

x = 216

Therefore, the total numbers of coins are 216,

Since, there are 1/2 of total coins are Asian coins,

Therefore, number of Asian coins = 216 / 2 = 108

Hence, There are total 108 coins belonging to Asian countries.

For more references on equations, click;

https://brainly.com/question/29657983

#SPJ2

Assume that Y is normally distributed with mean μ and standard deviation σ. After observing a value of Y, a mathematician will construct a rectangle with length L = |Y|and width W = 3 |Y|. Let A denote the area of the resulting rectangle. What is E(A)?

Answers

It would be 3L and ea poroption thanks for the points

Hi :), im really struggling with this. Just wanted to know if anyone can explain step by step for me please?

Answers

Answer:

314 m²

Step-by-step explanation:

the surface area of a sphere (As) = 4×pi×r²

our radius r (half the diameter) here is 5m.

=>

As = 4×pi×5² = 4×3.14×25 = 100×3.14 = 314 m²

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