statistics problem

8/10/2019 Statistics problem

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Home Assignment 1 :

Problem 1:Let A be the event that a person is female and B be the event that a person is short. If the i

ndividuals are chosen at random from a group of persons, we have the following probabilities;

P(A) !."#, P(B) !.$!, P(A%B) !.

'ind (i) P(AB), (ii)P(A B)U

, (iii)

c

P(A B) , (iv)

c

P(A B)U

, (v)

c c

P(A B ) (vi)

c c

P(A B )U

Problem 2:*hree fair coins are tossed and the upper face of each coin is recorded. Answer the followi

ng +uestions.

(a) ow man- sample points are in the sample space onstruct a tree diagram to list the sample spac

e.

(b) /hat is the probabilit- of getting e0actl- one head

(c) /hat is the probabilit- of getting e0actl- two heads

(d) /hat is the probabilit- of getting at least one head

(e) /hat is the probabilit- of getting no heads

(f) /hat is probabilit- of getting at least one tail

Problem 3: *wo fair dice are tossed, and the number of dots on upper faces of the dice are observed.

'ind the probabilities of the following events;

(a) the sum of two numbers is e+ual to "

(b) ths sum of two numbers is e+ual to 1

(c) the sum of two numbers is e+ual to 2

Problem 4: 3uppose a bag contains balls, of which # are white, 4 are blac5 and " are red. *wo bals

s are successivel- drawn at random from the bag without replacement. 'ind the probabilit- of the foll

wing events;

(a) first ball is white

(b) second ball is white given the first ball is white

(c) the first ball is white and the second ball is white

(d) the first ball is blac5

(e) the second ball is white given the first ball is blac5

(f) the first ball blac5 and the second ball is white

Problem 5 : Let A and B are two events and their probabilities are as P(A) !.6#, P(B) !.1# and P(A

%B) !.#! . 'ind the probabilities of the following events;

'ind

(i) P(AB), (ii) P(A B)U , (iii) P(B%A) , (iv) either A or B or both occur, (v) Are A and B independent

(vi) Are A and B mutuall- e0clusive, (vii) Are A and B e0haustive

Problem 6. 3uppose there is a group of &!! third -ear students at the 7epartment of 8conomics, of wh

ich &! female students have obtained A grade in both first term and second term e0aminations, # male

students have obtained A grade in both first term and seccond e0aminations, $# female students have o

btained B grade in both first term and second term e0aminations, $! male students have obtained B

grade in both e0aminations, &! female students have obtained grade in both e0aminations, and m

ale students have obtained in both e0aminations. If a student is selected at random from the group,

(a) what is the probabilit- that the student is male

(b) what is the probabilit- that the student is female

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(c) what is the probabilit- that the student is female or obtained A grade in both first term and second t

erm e0aminations

(d) what is the probabilit- the student is male or obtained A grade in both e0aminations

(e) what is the student has obtained A grade given the student is female

(f) what is the probabilit- that the student has obtained B grade given the student is male

Problem 7 : A sales manager of a compan- is interested to 5now the effect of *9 advertisement on sal

e of his compan-:s products. 'or this purpose, he randoml- selected the persons and results of the resp

ondents are given with the following table;

8vents /atched *9 Advertisement

(A)

7id ot /atch *9 Advertiseme

nt ( cA )

Purchased Product (B) #! 4!

7id ot Purchase Product( cB ) "! &!!

'ind the following probabilities

(i) P(A), (ii) P( cA ), (iii) P(B), (iv) P( cB ), (v) P(B%A), (vi) ( )P A BU , (vi) P(AB)

(g) Is there positive effect of watching the *9 advertisement on products sale

Problem 8 : *he tea compan- is interested to 5now the situation of the demand of different barands of

tea. *herefore mar5eting officer surve- the mar5et, ! individuals as5ed for their preference among t

hree different brands Lipton (A), Ispahani (B) and *ata () of tea. *he respondents are classified acco

rding to their famil- income, igh Income


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Problem 10. 3uppose the three garments suppl- leather ?ac5ets in the 3A. *he garment A suppl- 4!

percent of their production ?ac5ets, garment B suppl- $# percent of their production ?ac5ets and garme

nt suppl- remaining 6# percent of their production ?ac5ets. But the percentages of defective ?ac5ets s

upplied b- these three companies are !.!", !.!# and and !.!$ respectivel-. *o chec5 the +ualit- of the t

hese leather ?ac5ets supplied b- these garments, an inspector has drawn a ?ac5et from the lots randoml

- and it is found to be defective. /hat is the probabilit- that the item is supplied b- A B- B and B-

Problem && *he medical team of 7ha5a =edical ollege is interested about the lung cancer and tuber

culosis of the population of 7ha5a it-. 'or this a person is selected at random from the cit- and given

a chest Cra-, and the results turn to be a positive. 'or the sa5e of simplicit- assume that the person co

uld have lung cancer, tuberculosis, or neither. *he follong information is available;

(i) *he probabilit- that a person with lung cancer will have a positive chest Cra- is !.>#

(ii) *he probabilit- that a person with tuberculosis will have a positive chest Cra- is !.>1

(iii) *he probabilit- that a person has neither lung cancer nor tuberculosis will have a postive chest Cra- is !.!#

(iv) # percent of the people of the population of 7ha5a it- have lung cancer and $ percent

have tuberculosis and the remaining have neither both of diseases.

/hat is the probabilit- that a person has lung cancer, tuberculosis or neither will have a postive chest

Cra-

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statistics problem

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