You're at a clothing store that dyes your clothes while you wait. You get to pick from

4

44 pieces of clothing (shirt, pants, socks, or hat) and

3

33 colors (purple, blue, or orange).

If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with socks that aren't blue?

The probability that you'll end up with socks that aren't blue is .

Step-by-step explanation:

The pieces of clothing available:

X = {shirt, pants, socks and hat}

The color options:

Y = {purple, blue and orange}

So, if a person picks a shirt he/she has 3 color options.

Similarly for pants, socks and hat there are 3 color options each.

That makes 12 possible pieces of clothing.

That is, there are 12 total options available.

Now, compute the probability of selecting a socks as follows:

Compute the probability of selecting the color blue as follows:

Compute the probability of selecting a socks that are not blue as follows:

Thus, the probability that you'll end up with socks that aren't blue is .