A drawer has 4 red socks and 2 blue socks. What is the probability of a match after picking 2 socks?

Probability of picking a matching pair would be 2 reds OR 2 blues

To find the probability of picking a matching pair of socks, we first need to determine the total number of possible outcomes when picking 2 socks from the drawer.

Total number of socks = 4 (red socks) + 2 (blue socks) = 6 socks

The number of ways to pick 2 socks out of 6 is calculated using combinations, which is denoted as ( C(n, k) = \frac{n!}{k!(n-k)!} ), where ( n ) is the total number of items, and ( k ) is the number of items to be chosen.

( C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5 \times 4!}{2 \times 4!} = \frac{6 \times 5}{2 \times 1} = 15 )

So, there are 15 possible outcomes when picking 2 socks from the drawer.

Now, let's calculate the number of outcomes where we pick a matching pair of socks.

Number of ways to pick 2 red socks out of 4 red socks = ( C(4, 2) = \frac{4!}{2!(4-2)!} = \frac{4 \times 3 \times 2!}{2 \times 2!} = \frac{4 \times 3}{2 \times 1} = 6 )

Number of ways to pick 2 blue socks out of 2 blue socks = ( C(2, 2) = \frac{2!}{2!(2-2)!} = \frac{2 \times 1 \times 1}{2 \times 1} = 1 )

Total number of outcomes with a matching pair = 6 (picking 2 red socks) + 1 (picking 2 blue socks) = 7

Now, the probability of picking a matching pair of socks is the number of outcomes with a matching pair divided by the total number of possible outcomes.

Probability = ( \frac{7}{15} )

So, the probability of picking a matching pair of socks is ( \frac{7}{15} ) or approximately 0.467.