Draw two cards in succession without replacement from a stan

Draw two cards in succession without replacement from a standard deck. Let A =

Solution

2 events are independent if

P(A and B) = P(A)*P(B)

P(Red on 1st draw) = 26/52 = 1/2

P(King on 2nd draw) = P(King on 2nd draw | King on 1st draw)*P(King on 1st draw) + P(King on 2nd draw | Non-King on 1st draw)*P(Non-King on 1st draw) = 4/52*3/51 + 48/52*4/51 = 1/13

P(Red on 1st draw and King on 2nd draw) = P(red king on 1st and king on 2nd) + P(red non-king on 1st and king on 2nd)

=2/52*3/51 + 24/52*4/51 = 1/26

= 1/2 * 1/13 = P(red on 1st) *P(king on 2nd)

Hence, the 2 events are independent