Urban Software Company with 48 employees has a company picni

Urban Software Company with 48 employees has a company picnic with two prize drawings. The door prize uses sampling with replacement (i.e. if a name is selected from the drawing, it is placed back in the bag) so that employees have a chance to win multiple door prizes. The grand prize drawing uses sampling without replacement (i.e. if a name is drawn, it is set aside before the next name is drawn) because the employees are not allowed to win multiple grand prizes.

Answer the following questions based on this scenario.

a) What is the probability that Gary, an employee, wins a door prize?

b) Gary wins a door prize. What is the probability that he will win a second door prize?                                                                                                           

c) There are 6 employees in the marketing department of Urban Software. What is the probability that one of the members of the marketing department wins the first grand prize?                          

d) If a member of the marketing department wins the first grand prize, what is the probability that another member of the marketing department wins the second grand prize?

Solution

given total number of employees is 48

then probability of each employee getting a door prize is 1/48

hence

(A) probability that gary won a door prize =1/48

B) if gary won the door prize then probability that he will win second door prize

since door prize given with replacement then in each chance they have equal chance of winning

hence required P=1/48

(C)

marketing department have 6 members then probability of winning one grand prize is 6/48=1/48

(D)if marketing dept won a grand prize then prob taht they win second grand prize

since grand prize given without replacement then required probability is

5/47=5/47ans