cant solve a probability - expected value question

cant solve a probability - expected value question

It doesnt seems like a hard question, but I cant get the correct answer.
maybe I got one of the basics steps wrong?
The question : A box contains 5 balls, numbered 1 to 5. i.e, {1,2,3,4,5}
first step : randomly choose a ball, and color that ball in black along
with all of the balls with numbers that are smaller than the first ball
number. (if we randomly drewed ball number 3 then we color balls 1,2,3 in
black)
the rest of the balls - we color in white.
second step : we choose again a random ball, what is the expected value of
the number of balls with the same color as the ball we drew?
I used conditional probability and got 2.6, the answer should be 3.4
(homework question)
what I did was to calculate the probability of drewing a black ball (3/5)
and a white ball (2/5) and
$EN=\sum_0^5 nP(n=N)=\sum_0^5 nP(N=n„ 2nd-black)P(2nd-black) + \sum_0^5
nP(N=n„ 2nd-white)P(2nd- white)$
now for $n=1,...,5$ each $P(N=n„ 2nd-black)=1/5$
and for white - $n=1,...,4$ each $P(N=n„ 2nd-white)=1/5$ aswell (because
they depends on the first ball number, and its random 1/5)
calculated all and got 2.6, the paper says 3.4 cant locate my error
any ideas? thanks for your time