Question and Answers Forum

Probability and StatisticsQuestion and Answers: Page 1

Question Number 206514 Answers: 0 Comments: 0

In this covid −19 pandemic, it is known that are 5,667,355 confirmed cases out of 273,500,000 in X country population based WHO. One of the equipment to test the covid−19 is GeNose C19−S developed by UGM. GeNose C19−S is a rapid screening equipment for Sars−CoV2 virus infection through the breath of Covid −19 patient . It is claim that the sensivity of the test is 0,90 that is, if a person has the disease, then the probability that the diagnostic blood test comes back positive is 0,90. In addition , the specificity of the test is 0,95, i.e if a person is free the disease, then the probability that the diagnostic test comes back negative is 0,95. Let D and H is the event that a randomly selected individual has the disease and disease−free (healty), respectively. a. What is the positive predictive value of the GeNose C19−S test? That is, given that the blood test is positive for disease, what is the probability that person actually has the disease? b. If the doctor perfoms the test for the second time , taking P(D) equals to the value of probability you obtained from part a), determine the update positive predictive value of the test.

$$\:{In}\:{this}\:{covid}\:−\mathrm{19}\:{pandemic},\:{it}\:{is}\: \\ $$$$\:{known}\:{that}\:{are}\:\mathrm{5},\mathrm{667},\mathrm{355}\:{confirmed}\: \\ $$$$\:{cases}\:{out}\:{of}\:\mathrm{273},\mathrm{500},\mathrm{000}\:{in}\:{X}\:{country} \\ $$$$\:{population}\:{based}\:{WHO}.\: \\ $$$$\:{One}\:{of}\:{the}\:{equipment}\:{to}\:{test}\:{the} \\ $$$$\:{covid}−\mathrm{19}\:{is}\:{GeNose}\:{C}\mathrm{19}−{S}\:{developed} \\ $$$$\:{by}\:{UGM}.\:{GeNose}\:{C}\mathrm{19}−{S}\:{is}\:{a}\:{rapid} \\ $$$$\:{screening}\:{equipment}\:{for}\:{Sars}−{CoV}\mathrm{2} \\ $$$$\:{virus}\:{infection}\:{through}\:{the}\:{breath} \\ $$$$\:{of}\:{Covid}\:−\mathrm{19}\:{patient}\:.\:{It}\:{is}\:{claim} \\ $$$$\:{that}\:{the}\:{sensivity}\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{90} \\ $$$$\:{that}\:{is},\:{if}\:{a}\:{person}\:{has}\:{the}\:{disease},\: \\ $$$$\:{then}\:{the}\:{probability}\:{that}\:{the}\:{diagnostic} \\ $$$$\:{blood}\:{test}\:{comes}\:{back}\:{positive} \\ $$$$\:{is}\:\mathrm{0},\mathrm{90}.\:{In}\:{addition}\:,\:{the}\:{specificity} \\ $$$$\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{95},\:{i}.{e}\:{if}\:{a}\:{person}\: \\ $$$$\:{is}\:{free}\:{the}\:{disease},\:{then}\:{the}\:{probability} \\ $$$$\:{that}\:{the}\:{diagnostic}\:{test}\:{comes}\:{back} \\ $$$$\:{negative}\:{is}\:\mathrm{0},\mathrm{95}.\: \\ $$$$\:{Let}\:{D}\:{and}\:{H}\:{is}\:{the}\:{event}\:{that}\:{a}\: \\ $$$$\:{randomly}\:{selected}\:{individual}\:{has} \\ $$$$\:{the}\:{disease}\:{and}\:{disease}−{free}\: \\ $$$$\:\left({healty}\right),\:{respectively}. \\ $$$$\:{a}.\:{What}\:{is}\:{the}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{GeNose}\:{C}\mathrm{19}−{S}\:{test}? \\ $$$$\:\:{That}\:{is},\:{given}\:{that}\:{the}\:{blood}\:{test}\: \\ $$$$\:{is}\:{positive}\:{for}\:{disease},\:{what}\:{is}\:{the} \\ $$$$\:{probability}\:{that}\:{person}\:{actually}\:{has} \\ $$$$\:\:{the}\:{disease}?\: \\ $$$$\: \\ $$$$\:{b}.\:{If}\:{the}\:{doctor}\:{perfoms}\:{the}\:{test}\:{for} \\ $$$$\:{the}\:{second}\:{time}\:,\:{taking}\:{P}\left({D}\right)\:{equals} \\ $$$$\:{to}\:{the}\:{value}\:{of}\:{probability}\:{you} \\ $$$$\left.\:{obtained}\:{from}\:{part}\:{a}\right),\:{determine}\: \\ $$$$\:{the}\:{update}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{test}.\: \\ $$

Question Number 205409 Answers: 0 Comments: 0

let x, y, z be random numbers from 0 to 10 where x,y,z∈R what is the probability that a) all the following is satisfied ∣x−y∣≥2 ∣x−z∣≥2 ∣y−z∣≥2 b) the probability that one or two of them are not satisfied c) the probability that all of them are not satisfied

$$\mathrm{let}\:{x},\:{y},\:{z}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y},{z}\in\mathbb{R} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\left.{a}\right)\:\mathrm{all}\:\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{satisfied} \\ $$$$\mid{x}−{y}\mid\geqslant\mathrm{2} \\ $$$$\mid{x}−{z}\mid\geqslant\mathrm{2} \\ $$$$\mid{y}−{z}\mid\geqslant\mathrm{2} \\ $$$$\left.{b}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\:\mathrm{one}\:\mathrm{or}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$\left.{c}\right)\:\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{all}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are}\:\mathrm{not}\:\mathrm{satisfied} \\ $$$$ \\ $$

Question Number 205394 Answers: 1 Comments: 0

let x and y be random numbers from 0 to 10 where x,y∈R ∣x−y∣≥d what is the probability that their sum is less than 10 in the following cases a) d=0 b) d=1 c) d=2

$$\mathrm{let}\:{x}\:\mathrm{and}\:{y}\:\mathrm{be}\:\mathrm{random}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{0}\:\mathrm{to}\:\mathrm{10} \\ $$$$\mathrm{where}\:{x},{y}\in\mathbb{R} \\ $$$$\mid{x}−{y}\mid\geqslant{d} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{10} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{cases} \\ $$$$\left.{a}\right)\:{d}=\mathrm{0} \\ $$$$\left.{b}\right)\:{d}=\mathrm{1} \\ $$$$\left.{c}\right)\:{d}=\mathrm{2} \\ $$

Question Number 205230 Answers: 0 Comments: 1

$$ \\ $$

Question Number 201972 Answers: 1 Comments: 0

Question Number 201969 Answers: 2 Comments: 0

A dice is cast twice, and the sum of the appearing numbers is 10. The probability that the number 5 has appeared at least once is.

$$\mathrm{A}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{cast}\:\mathrm{twice},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{appearing}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{10}. \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\:\mathrm{5}\:\mathrm{has}\: \\ $$$$\mathrm{appeared}\:\mathrm{at}\:\mathrm{least}\:\mathrm{once}\:\mathrm{is}. \\ $$

Question Number 201545 Answers: 0 Comments: 0

Question Number 201527 Answers: 1 Comments: 0

Question Number 201475 Answers: 0 Comments: 5

Question Number 201439 Answers: 0 Comments: 0

There is a field. Everyday kids throw some balls on the field. At night the farmer goes and place the bucket in a place where it will contain the most amount of balls. the field can be represented as a line of length 10. the bucket can be represented as a line of length 2. If the kids have thrown 3 balls into the field, what is the probability that the bucket will contain 2 balls how a sample looks like Where the blue line represents the field. and the red line represents the bucket. and the dots are the balls

$$ \\ $$$$ \\ $$There is a field. Everyday kids throw some balls on the field. At night the farmer goes and place the bucket in a place where it will contain the most amount of balls. the field can be represented as a line of length 10. the bucket can be represented as a line of length 2. If the kids have thrown 3 balls into the field, what is the probability that the bucket will contain 2 balls $$\mathrm{how}\:\mathrm{a}\:\mathrm{sample}\:\mathrm{looks}\:\mathrm{like} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$Where the blue line represents the field. and the red line represents the bucket. and the dots are the balls $$ \\ $$

Question Number 200831 Answers: 0 Comments: 1

Question Number 200720 Answers: 2 Comments: 0

Question Number 199714 Answers: 0 Comments: 3

Statement Does the number of data have to be more than 100 in order to have a percentile value ?

$$\:{Statement}\: \\ $$$$\:{Does}\:{the}\:{number}\:{of}\:{data}\:{have} \\ $$$$\:{to}\:{be}\:{more}\:{than}\:\mathrm{100}\:{in}\:{order}\: \\ $$$$\:{to}\:{have}\:{a}\:{percentile}\:{value}\:? \\ $$

Question Number 199446 Answers: 0 Comments: 0

53bxnx

$$\mathrm{53bxnx} \\ $$

Question Number 199310 Answers: 1 Comments: 1

What is the probability that in a class of 18 people, there exists a group of 3 people born on the same day of the week?

$${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{a}\:{group}\:{of}\:\mathrm{3} \\ $$$${people}\:{born}\:{on}\:{the}\:{same}\:{day}\:{of}\:{the} \\ $$$${week}? \\ $$

Question Number 198975 Answers: 0 Comments: 7

60 students of a school must take at least one of the three courses for mathematics, physics and chemistry respectively. if a student is randomly picked, what is the probability that he/she takes only one course?

$$\mathrm{60}\:{students}\:{of}\:{a}\:{school}\:{must}\:{take} \\ $$$${at}\:{least}\:{one}\:{of}\:{the}\:{three}\:{courses}\:{for} \\ $$$${mathematics},\:{physics}\:{and}\:{chemistry} \\ $$$${respectively}. \\ $$$${if}\:{a}\:{student}\:{is}\:{randomly}\:{picked},\:{what} \\ $$$${is}\:{the}\:{probability}\:{that}\:{he}/{she}\:{takes} \\ $$$${only}\:{one}\:{course}? \\ $$

Question Number 198879 Answers: 0 Comments: 0

Question Number 198141 Answers: 1 Comments: 0

∫^( 1) _( 0) ((x(1−x))/(sin(πx)))dx=???

$$\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \:\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{x}\right)}{\mathrm{sin}\left(\pi\mathrm{x}\right)}\mathrm{dx}=??? \\ $$

Question Number 196916 Answers: 0 Comments: 0

Question Number 196447 Answers: 2 Comments: 0

n! = 2^(25) ×3^(13) ×5^6 ×7^4 ×11^2 ×13^2 ×17×19×23 n=?

$$\:\:\:\:\mathrm{n}!\:=\:\mathrm{2}^{\mathrm{25}} ×\mathrm{3}^{\mathrm{13}} ×\mathrm{5}^{\mathrm{6}} ×\mathrm{7}^{\mathrm{4}} ×\mathrm{11}^{\mathrm{2}} ×\mathrm{13}^{\mathrm{2}} ×\mathrm{17}×\mathrm{19}×\mathrm{23} \\ $$$$\:\:\:\mathrm{n}=? \\ $$

Question Number 194490 Answers: 1 Comments: 0

A research station supplies three varieties of seeds S1, S2 and S3 in the ratio 4: 2: 1. The probabilities of germination of S1, S2 and S3 are 50%, 60% and 80% respectively. Find the probability that a seed selected at random will germinate.

$$\mathrm{A}\:\mathrm{research}\:\mathrm{station}\:\mathrm{supplies}\:\mathrm{three}\:\mathrm{varieties}\: \\ $$$$\mathrm{of}\:\mathrm{seeds}\:\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{4}:\:\mathrm{2}:\:\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{probabilities}\:\mathrm{of}\:\mathrm{germination}\:\mathrm{of}\: \\ $$$$\mathrm{S1},\:\mathrm{S2}\:\mathrm{and}\:\mathrm{S3}\:\mathrm{are}\:\mathrm{50\%},\:\mathrm{60\%}\:\mathrm{and}\:\mathrm{80\%} \\ $$$$\mathrm{respectively}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{a}\:\mathrm{seed}\:\mathrm{selected}\:\mathrm{at}\:\mathrm{random}\:\mathrm{will}\:\mathrm{germinate}. \\ $$

Question Number 194292 Answers: 0 Comments: 0

Question Number 193351 Answers: 0 Comments: 0

Question Number 193350 Answers: 0 Comments: 0

Question Number 193292 Answers: 1 Comments: 0

(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same color. (b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?

$$ \\ $$(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are not of the same color. (b) A man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship. He returns by the same means. He has 6 airlines and 4 shipping lines to choose from. In how many ways can he make his journey without using the same airline or shipping line twice?

Question Number 193226 Answers: 1 Comments: 0

(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

$$ \\ $$(a) 5 out of 12 articles are known to be defective. If three articles are picked, one after the other, without replacement, find the probability that all the three articles are non-defective. (b) Two coins are tossed and a dice is thrown. What is the probability of obtaining a head, a tail and a 4?

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

Contact: info@tinkutara.com