Question

An person has applied for positions at Company A, Company B and Company C. The probability of obtaining an offer from Company A is 0.3, from Company B is 0.6 and from Company C is 0.8. Assume that the three job offers are independent.

A)What is the probability that the person will receive a job offer from ALL three companies?

B)What is the probability that the person will receive a job offer from Company A only ?

C)What is the probability that the person will receive job offer from Company B only ?

D)What is the probability that the person will receive job offer from Company C only ?

E)What is the probability that the person will receive a job offer from exact one company (either A, B or C)?

F)What is the probability that the person will receive a job offers from Company A and B but not C?

G)What is the probability that the person will receive a job offers from Company A and C but not B?

H)What is the probability that the person will receive a job offers from Company B and C but not A?

I)What is the probability that the person will receive a job offers from exactly two companies?

K)What is the probability that the person will not receive any job offers?

L)What is the probability that the person will receive at least one job offer (i.e. either 1 or more)?

(PLZ ANSWER ASAP)

Answer 1

P(A) = 0.3

P(B) = 0.6

P(C) = 0.8

A)What is the probability that the person will receive a job offer from ALL three companies?

probability that the person will receive a job offer from ALL three companies = P(A)*P(B)*P(C)

probability that the person will receive a job offer from ALL three companies = 0.3*0.6*0.8

probability that the person will receive a job offer from ALL three companies = 0.144

B)What is the probability that the person will receive a job offer from Company A only ?

probability that the person will receive a job offer from Company A only = P(A)*(1-P(B))*(1-P(C))

probability that the person will receive a job offer from Company A only = 0.3*(1-0.6)*(1-0.8)

probability that the person will receive a job offer from Company A only = 0.3*0.4*0.2

probability that the person will receive a job offer from Company A only = 0.024

C)What is the probability that the person will receive job offer from Company B only ?

probability that the person will receive job offer from Company B only = P(B)*(1-P(A))*(1-P(C))

probability that the person will receive job offer from Company B only = 0.6*(1-0.3)*(1-0.8)

probability that the person will receive job offer from Company B only = 0.6*0.7*0.2

probability that the person will receive job offer from Company B only = 0.084

D)What is the probability that the person will receive job offer from Company C only ?

probability that the person will receive job offer from Company C only = P(C)*(1-P(A))*(1-P(B))

probability that the person will receive job offer from Company C only = 0.8*(1-0.3)*(1-0.6)

probability that the person will receive job offer from Company C only = 0.8*0.7*0.4

probability that the person will receive job offer from Company C only = 0.224

E)What is the probability that the person will receive a job offer from exact one company (either A, B or C)?

probability that the person will receive a job offer from exact one company (either A, B or C) = probability that the person will receive job offer from Company A only + probability that the person will receive job offer from Company B only + probability that the person will receive job offer from Company C only

probability that the person will receive a job offer from exact one company (either A, B or C) = 0.024 + 0.224 +0.084

probability that the person will receive a job offer from exact one company (either A, B or C) = 0.332

F)What is the probability that the person will receive a job offers from Company A and B but not C?

probability that the person will receive a job offers from Company A and B but not C = P(A)*P(B)*(1-P(C))

probability that the person will receive a job offers from Company A and B but not C = 0.3*0.6*(1-0.8)

probability that the person will receive a job offers from Company A and B but not C = 0.3*0.6*0.2

probability that the person will receive a job offers from Company A and B but not C = 0.036

G)What is the probability that the person will receive a job offers from Company A and C but not B?

probability that the person will receive a job offers from Company A and C but not B = P(A)*P(C)*(1-P(B))

probability that the person will receive a job offers from Company A and C but not B = 0.3*(1-0.6)*0.8

probability that the person will receive a job offers from Company A and C but not B = 0.3*0.8*0.4

probability that the person will receive a job offers from Company A and C but not B = 0.096

H)What is the probability that the person will receive a job offers from Company B and C but not A?

probability that the person will receive a job offers from Company B and C but not A = P(B)*P(C)*(1-P(A))

probability that the person will receive a job offers from Company B and C but not A = 0.6*0.8*(1-0.3)

probability that the person will receive a job offers from Company B and C but not A = 0.6*0.8*0.7

probability that the person will receive a job offers from Company B and C but not A = 0.336

I)What is the probability that the person will receive a job offers from exactly two companies?

probability that the person will receive a job offers from exactly two companies = probability that the person will receive a job offers from Company A and B but not C + probability that the person will receive a job offers from Company A and C but not B + probability that the person will receive a job offers from Company B and C but not A

probability that the person will receive a job offers from exactly two companies = 0.036 + 0.096 + 0.336

probability that the person will receive a job offers from exactly two companies = 0.468

K)What is the probability that the person will not receive any job offers?

probability that the person will not receive any job offers = (1-P(A))*(1-P(B))*(1-P(C))

probability that the person will not receive any job offers = (1-0.3)*(1-0.6)*(1-0.8)

probability that the person will not receive any job offers = 0.7*0.4*0.2

probability that the person will not receive any job offers = 0.056

L)What is the probability that the person will receive at least one job offer (i.e. either 1 or more)?

probability that the person will receive at least one job offer (i.e. either 1 or more) = 1 - probability that the person will not receive any job offers

probability that the person will receive at least one job offer (i.e. either 1 or more) = 1 - 0.056

probability that the person will receive at least one job offer (i.e. either 1 or more) = 0.944