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Ugo [173]
3 years ago
8

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?
Mathematics
1 answer:
LenKa [72]3 years ago
3 0

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.

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

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

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

There are five multiple choice questions on the exam.

This means that n = 5

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 p = \frac{1}{4} = 0.25

a. Five questions correct?

This is P(X = 5). So

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

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

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

b. At least four questions correct?

This is:

P(X \geq 4) = P(X = 4) + P(X = 5)

So

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

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

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

P(X \geq 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.001 = 0.0156

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

c. No questions correct?

This is P(X = 0). So

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

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

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

d. No more than two questions correct?

This is:

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2). So

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

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

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

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

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965

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

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These 2 questions confuse me.<br> Can anyone help with some 3D trigonometry?
Burka [1]

Answer:

Q2) 29 degree       as unrounded to nearest degree is 28.95 degree

Q3) 69 degree       as unrounded to nearest degree is 68.56 degree

Step-by-step explanation:

QU 2)

When they speak of plane we see ABCD and also see ABC

So we need the length of AB and BC to find the diagonal CA

AB^2 + BC^2 = CA^2

16.4^2 + 9.1^2 = sqrt 351.77

CA^2 = sqrt 351.77 = 18.8 cm

We know CG = 10.4cm

We identify the hypotenuse for ACG triangle

We do trig tan x = opp/adj for CGA angle

Tan x = tan-1 10.4/18.8 = 28.95099521 degree

Tan x = tan-1 18.8/10.4 = 61.04900479 degree

so we know one is much smaller than the other

We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.

Answer therefore must be 28.95 degree = or 29 degree

 

QU 3)

we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.

= 7.6/2 = 3.8 cm

Then Pythagoras

BV^2  -  1/2 BC =  height

10.4^2  - 3.8^2 = height

Height = sq rt 93.72 =9.68090905 = 9.7cm

Which means  V to midpoint VC = V to midpoint  AB

They are the same and the midpoints are 90 degree angles.

To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.

We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp

Because if it was the midpoint angle then it would be opp/adj like the question 1  so this time its cos of x.

cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455

Answer is 68.56 degree

The reason we show the height is so we can check by doing opp/hyp

= sin of x = sin-1 (9.68090905/3.8) = 23.11171135

and 90 -23.11171135 = 66.8882887

= 67 degree

So we go with the first one and assume 9.68 was already simplified to 9.7cm

= sin-1 (3.8/9.7) = 23 degree  90-23 = 67 degree

but when rounded to 10.4cm for slant we get the same

= sin-1 (3.8/10.4)

So we realise here trig functions -1  doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.

We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree

and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.

This proves that cos line 1/line2  = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di

and smallest side acts as denominator for both trig functions.

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3 years ago
You run a software company and hired a new salesperson. You offer $40,000 base salary. Additionally, if the salesperson sells $5
oee [108]
The answer is $45,000.
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3 years ago
(a) An angle measures 140 . What is the measure of its supplement? (b) An angle measures 36 . What is the measure of its complem
Lesechka [4]
A: 40 because supplements add up to 180
B: 54 because complements add up to 90
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A new lawn has a perimeter of 278ft. And a width of 64ft. A bag of grass seed will cover 384ft of ground. How many bags of grass
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Answer:

13 bags

Step-by-step explanation:

Area of the lawn: A=lw

w= 64 ft

P= 2(l+w)= 278 ft ⇒

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bags of seed required:

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7 0
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Please help ASAP. I am confused
Lesechka [4]

Answer:

So if ∠X is 70° then ∠Y is most likely going to be 70° as well. So if you take 180° which is a straight line and subtract both of the 70°'s you'd get 40°. This answer seems pretty accurate to me.

Step-by-step explanation:

Hope this helps you out! :)

(If any question s put them below and I'll try my best to answer them)

3 0
2 years ago
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