A card is drawn from a well shuffled pack of 52 cards. Its outcome is noted and then another card is drawn without replacing the first card. The probability that the first card is heart and second card is red ace is:

$\frac{25}{2652}$

The correct answer is Option (4) - $\frac{25}{2652}$

No. of cards in first draw = 52

so probability of getting hearts = $\frac{13}{52}$

P getting non ace heart = $\frac{12}{52}$

Now 51 cards remaind

in case first card was a red ace

then P(ace in 2nd draw) = $\frac{1}{51}$

in case it wasn't P(ace in 2nd draw) = $\frac{2}{51}$

So total probability = P(non ace hearts) × P(ace in 2nd drawn) + P(ace heart) × P(ace in 2nd drawn)

$=\frac{12}{52}×\frac{2}{51}+\frac{1}{52}×\frac{1}{51}=\frac{25}{2652}$