A standard deck of cards consists of 26 red cards (hearts and diamonds) and 26 black cards (clubs and spades). Suppose you shuffle such a deck and draw three cards at random without replacement. Let $A_i =$ the event that the $i$th card is a red card, for $i = 1, 2, 3$. Mark each of the following statements as TRUE or FALSE.
(a) $P(A_2)> P(A_1)$
(b) $A_1$ and $A_3$ are independent.
(c) $P(A_1|A_3)< P(A_1)$
I'm having a lot of trouble with part a. Obviously $P(A_1)$ is $26/52$, but $P(A_2)$ is either ($26/51$) or ($25/51$) depending on what happened in $A_1$.