Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is a king, the second card is hearts, and the third card is red.
Since there are $4$ kings from a deck of $52$ cards, the probability that the first card drawn is a king is $\dfrac{4}{52}=\dfrac{1}{13}$. Since there are $13$ hearts in a deck of $52$ cards, the probability that the second card drawn will be hearts is $\dfrac{13}{51}$, since only $51$ cards remain after one card is drawn. Since there are $26$ red cards at the beginning, the probability that the third card drawn is red is $\dfrac{26}{50}$. Now we multiply these probabilities together to get the probability that all three events occur: $$\dfrac{1}{13} \cdot \dfrac{13}{51} \cdot \dfrac{26}{50}=\boxed{\dfrac{1}{100}}.$$
