Question

Choice leads for developing new business opportunities are randomly assigned to 50 employees who make up the sales team. Half of the sales team is male, and half is female. An employee can receive at most one choice lead per day. On a particular day, five choice leads are assigned. (a) Are the events (first lead given to a male) and (second lead given to a male) dependent or independent? (b) If the first four leads all go to men, what is the probability that the fifth lead also goes to a man? (c) What is the probability that all five leads go to men if you know that at least four of the leads go to men? (This item is harder than most. A procedure to handle these sorts of problems is given in Chapter 11, but you can do this exercise from principles in this chapter.)

Answer 1

Answer:

Step-by-step explanation:

50 employees make up the sales team, 25 male and 25 female, 5 choice leads are assigned

a)

p(first lead given to male)=25/50

p(second lead given to male)=24/49

Since the probabilities of first and second are not affected by each other, the events are independent

b)

Given that first four leads go to men

Therefore, number of men left=21

number of employees left=46

p(fifth lead goes to man)=21/46

c)

At least four leads go to man, given

four leads are men

number of men left = 21

number of women left= 25

number of employes left = 46

probability= $\frac{^25C_5(all.5.men)}{^25C_5(all.5.men)+^25C_4(men)\imes ^25C_1(woman)}\\\\=\frac{21}{146}$