Question 442929
Let's count how many socks we have all together:

8 + 3 + 10 = 21.

We have {{{highlight(21)}}} socks.

Now how many blue socks do we have?

{{{highlight(8)}}}

So we have a {{{8/21}}} chance of drawing a blue sock.

We take a blue sock and we don't replace it.
How many socks do we have left? 20. How many blue socks do we have left? 7.

We have a 7/20 chance of drawing a blue sock.

So what is P(Blue Sock and Another Blue Sock) = P(Blue Sock) * P(Another Blue Sock) =  (8/21) * (7/20)

Let's simplify this:

To make this easier, let's take each term into it's prime decomposition. This is if you have trouble simplifying fractions.

{{{expr((2*2*2)/(3*7)) * expr(7/(2*2*5)) = expr((cross(2)*cross(2)*2)/(3*cross(7))) * expr(cross(7)/(cross(2)*cross(2)*5)) = expr(2/(3*5))=2/15}}}

If you aren't comfortable with that, then just multiply it straight out {{{(8*7)/(20*21) = 56/420 = (2*28)/(2*210) = (cross(2) * 28)/ (cross(2) *210) = (14*2) / (14 * 15) = (cross(14)*2)/(cross(14)*15) = 2/15}}}