Suppose a small firm has 40 accounts payable, of which 5 are type A accounts, 15

Question

Suppose a small firm has 40 accounts payable, of which 5 are type A accounts, 15 are type B accounts and 20 are type C accounts, it is known that 5 of the 40 accounts payable contain errors, none of which are of type A or B. For an internal audit, the auditor will randomly select 2 type A accounts, 3 type B accounts and 6 type C accounts. a. What is the probability that a random selection will contain exactly two accounts with errors? b. What is the probability that a random selection will contain at least one account with an error? Construct a probability model describing the following experiment: Families with 3-children are surveyed and the gender of the children are listed according to birth order. a. Find the probability of exactly 2 girls, given that the first child is a girl. b. Find the probability of exactly 1 girl, given that the first child is a boy. 3. The Chicago Black Hawks hockey team has a probability of winning of 0.6 and a probability of losing of .25. What is the probability of a tie?

Explanation / Answer

1)

Type A : 5 (2)

Type B : 15 (3)

Type C : 20 (6)

5 accounts of type C contains Error

a) exactly two accounts with error :

as type A and B accounts doesn't contain error so...combination of account picked from A and B..doesn't matter

So we have to find out probability for Type C only : 5C2/20C6

= (5*4/2)/(20*19*18*17*16*15/6*5*4*3*2)

=10/19*17*8 =0.0038

b) atleast 1 with error = 1- no error

= 1 - no error in type C

= 1 -  15C6/20C6

= 1 - (15*14*13*12*11*10 /6*5*4*3*2)/20*19*18*17*16*15/6*5*4*3*2)

= 1 - 0.129 = 0.87

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