Question

In: Statistics and Probability

An person has applied for positions at Company A, Company B and Company C. The probability...

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)

Expert Solution

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

orchestra answered 2 years ago

6. A student has applied for a job at Company X and Company Y. The probability...

6. A student has applied for a job at Company X and Company Y. The probability of getting the job at "X" is 0.45, and the probability of getting the job at "Y" is 0.20. Assuming that the job offers are independent of each other, what is the probability that: A. The student gets an offer from both companies? B. The student will get at least one offer? C. The student will not receive an offer from either company?

The probability that a person in the United States has type B+ blood is 10%. Five...

The probability that a person in the United States has type B+ blood is 10%. Five unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all five have type B+ blood.The probability that all five have type B+ blood is nothing. (Round to six decimal places as needed.) (b) Find the probability that none of the five have type B+ blood.The probability that none of the five have type...

Person B has visited Person B has not visited Total Person A has visited 2 0...

Person B has visited Person B has not visited Total Person A has visited 2 0 2 Person A has not visited 0 48 48 Total 2 48 50 Now suppose that one of the 50 states is selected at random, so each state has a 1/50 = .02 probability of being selected. Determine the conditional probability that A has visited the (randomly selected) state, given that the state lies to the west of the Mississippi River. Then determine this...

Each of persons A, B and C has a gun containing a single bullet. Each person,...

Each of persons A, B and C has a gun containing a single bullet. Each person, as long as she is alive, may shoot at any surviving person. First A can shoot, then B (if still alive), then C (if still alive). Denote by pi ∈ (0, 1) the probability that player i hits her intended target. Assume that each player wishes to maximize her probability of survival; among outcomes in which her survival probability is the same, she wants...

a)Suppose A and B are disjoint events where A has probability 0.5 and B has probability...

a)Suppose A and B are disjoint events where A has probability 0.5 and B has probability 0.4. The probability that A or B occurs is B) The expected return of a kind of stock is 12% with standard deviation 10%. The expected return of a kind of bond is 4% with standard deviation 2%. The covariance of the return of the stock and of the bond is -0.0016. What is the standard deviation of a portfolio of 20% invested in...

Three people A, B, and C practice shooting at a target. The probability that A, B,...

Three people A, B, and C practice shooting at a target. The probability that A, B, and C hit the target is 0.9, 0.8 and 0.6, respectively. 1) Now select any one of them at random, what is the probability that the person selected hits the target? 2) If the person actually hit target, what is the probability that the person selected is A? 3) If the person selected shoots once more, what is the probability that he hits the...

A test is designed to detect cancer. If a person has cnacer, then the probability that...

A test is designed to detect cancer. If a person has cnacer, then the probability that the test will detect it is .95; if the person does not have cancer, the probability that the test will erroneously indicate that he does have cancer is .1. Assume 15% of the population who take the test have cancer. What is t he probability that a person described by the test as not having cancer really does have it?

1. Three players, A,B, and C, each flip their coins until one person has a different...

1. Three players, A,B, and C, each flip their coins until one person has a different result from the others. The person having the different result wins. (a) Using R, simulate this experiment 10000 times and give the resulting estimate of P(A wins).

Define the following events: A-> person had flip flops on B-> Person had blonde hair C->...

Define the following events: A-> person had flip flops on B-> Person had blonde hair C-> Person had red hair D-> Person had black hair E-> Person had brown her a. What is P(B')? b. What is P(C U E)? c. What is P(A U C)? d. What is P(A intersection C)? e. What is P(A' intersection (B U D))? Define the following events: A-> coin lands on heads B-> die lands on a "1" a. How many unique outcomes...

A diagnostic test has a probability of 92% of giving a positive result when applied to...

A diagnostic test has a probability of 92% of giving a positive result when applied to a person suffering from a certain disease. The test has a probability of 5% of giving a false positive when applied to a non-sufferer. If 6% of the population suffer from the disease, what is the probability of a positive test result?