The following question involves a standard deck of $52$ playing cards. In such a deck of cards there are four suits of $13$ cards each. The four suits are: hearts, diamonds, clubs, and spades. The $26$ cards included in hearts and diamonds are red. The $26$ cards included in clubs and spades are black. The $13$ cards in each suit are: $2,3,4,5,6,7,8,9,10,$ Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four $10$s$,$ etc., down to four $2$s in each deck.

You draw two cards from a standard deck of $52$ cards without replacing the first one before drawing the second.

$($a$)$

Are the outcomes on the two cards independent? Why?

No$.$ The probability of drawing a specific second card depends on the identity of the first card.

No$.$ The events cannot occur together.

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.

Yes. The events can occur together.

$($b$)$

Find P$($king on $1$st card and jack on $2$nd$).($Enter your answer as a fraction.$)$

$($c$)$

Find P$($jack on $1$st card and king on $2$nd$).($Enter your answer as a fraction.$)$

$($d$)$

Find the probability of drawing a king and a jack in either order. $($Enter your answer as a fraction.$)$