Ten white socks and five red socks are in a drawer. if two socks are selected at random, what is the probability that both socks are the same color?

10 W  and 5 R.

Total = 10 + 5 = 15.

We would assume there is replacement. That is the probability of picking any color depends solely on the entire 15 socks. That is the total remains as 15, we don't reduce it by 1 when the one sock is picked out.

For the two colors to be the same:

It is either  WW or RR

P(W) =  10 / 15               P(R) = 5/15

P(W and W) = P(W) * P(W) =  10 / 15    *   10 / 15 = 2 / 3 * 2/3 = 4/9

 P(R and R) = P(R) * P(R) =  5 / 15    *   5 / 15 = 1 / 3 * 1/3 = 1/9 

P(WW) or P(RR) = P(WW)  +  P(RR)

                               =  4 / 9  + 1/9 =  (4 + 1) / 9 = 5 / 9

So probability that both socks are the same = 5 / 9

When we have "or" in probability we simply add. And if we have "and" we simply multiply.

Note that in solving this we have assumed that there is replacement. That the total remains as 15.

I hope this helped.