Question

There are a total of three orders that need mailed to three suppliers. The person mailing the orders messed up and all of the orders were sent to random suppliers. What is the probability that: a. No matches occur

b. Exactly one match occurs

Answer 1

Total number of orders = 3

Total number of suppliers = 3

The person mailing the orders messed up and all of the orders were sent to random suppliers.

The number of possible ways to send an order

	Supplier
	1	2	3
Order	1	2	3
	1	3	2
	2	1	3
	2	3	1
	3	1	2
	3	2	1

Total number of ways= 6

a) Let the event A is defined as

A : No mathches occur

The number of possible ways are

	Supplier
	1	2	3
Order	2	3	1
	3	1	2

The probability of an event A is

P ( No mathches occur) = 2/6 = 0.3333

b) The event B is defined as

B : Exactly one match occurs.

The number of possible ways are

	Supplier
	1	2	3
Order	1	3	2
	3	2	1
	2	1	3

Number of ways = 3

Hence

P(B) = P ( Exactly one match occur) = 3/6 = 1/2 = 0.5000