Question

counting outcomes
a drawer contains one pair of brown socks and one pair of white socks. the table shows the possible outcomes, or sample space, for choosing a sock, replacing it, and then choosing another sock. if the first sock is not replaced, how many possible outcomes are there? how many of these outcomes contain a matching pair of socks?

Explanation:

Step1: Calculate total outcomes

There are 4 socks initially. For the first - draw, there are 4 choices. Since the sock is not replaced, for the second - draw, there are 3 choices. By the multiplication principle of counting, the total number of possible outcomes is \(4\times3 = 12\).

Step2: Calculate number of matching - pair outcomes

Case 1: Brown pair. The number of ways to pick a brown sock first and then another brown sock is \(2\times1=2\) (2 brown socks to start with and then 1 left).
Case 2: White pair. The number of ways to pick a white sock first and then another white sock is \(2\times1 = 2\).
The total number of outcomes with a matching pair is \(2 + 2=4\).

Answer:

How many possible outcomes are there? 12
How many of these outcomes contain a matching pair of socks? 4