Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are king?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{1}{270725}$ ##
Let $E_1, E_2, E_3$ and $E_4$ are the events that the first, second, third and fourth card is king, respectively.
$∴P(E_1 \cap E_2 \cap E_3 \cap E_4) = P(E_1) \cdot P(E_2 | E_1) \cdot P(E_3 | E_1 \cap E_2) \cdot P[E_4 | (E_1 \cap E_2 \cap E_3)]$
$= \frac{4}{52} \cdot \frac{3}{51} \cdot \frac{2}{50} \cdot \frac{1}{49} = \frac{24}{52 \cdot 51 \cdot 50 \cdot 49}$
$= \frac{1}{13 \cdot 17 \cdot 25 \cdot 49} = \frac{1}{270725}$