If two cards are drawn from a well shuffled pack, the probability that atleast one of the two is heart is

Random experiment is " Drawing two cards from well shuffled pack of cards"

Let $S$ be the sample space, $n\left(S\right)={52}_{C_2}=\frac{52·51}{2}=26·51$

Let $E$be the event of getting at least one heart card.

The compliment event of $E$ is $\overline{E}$, this is the event of getting no heart card

Since there are 13 heart cards, $n\left(\overline{E}\right)={39}_{C_2}=\frac{39·38}{2}=39·19$

Hence, $P\left(\stackrel{\rightharpoonup }{E}\right)=\frac{n\left(\overline{E}\right)}{n\left(S\right)}=\frac{39·19}{26·51}=\frac{19}{34}$

Therefore, the probability of getting at least one heart is 

     $\begin{array}{rcl}P\left(E\right)& =& \frac{n\left(E\right)}{n\left(S\right)}=1-\frac{n\left(\overline{E}\right)}{n\left(S\right)}\\ & =& 1-\frac{19}{34}\\ & =& \boxed{\frac{15}{34}}\end{array}$