counting outcomes\na drawer contains one pair of brown socks and one pair of white socks. the table shows…

counting outcomes\na 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?

counting outcomes\na 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?

Answer

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