Problem $7$

Consider the experiment where you select one card at a time, at random and without replacement, from a playing $52-$card deck $(13$ cards per suit$).$

Let $H_i$ be the event that a heart is the $i$ th draw from the deck.

Compute $P(H_1).$

Compute $P(H_2)($hint$.$ conditioning on the first card drawn from the deck. and use the law of total probability$)$

Hint: find a set of events that partitions the sample space, be clear in naming these events. For instance, $\{H,S,D,C\}$ can be the set of events that indicate hearts, spade, diamond, club. $\{1,2,$dots,$13\}$ can be ace, two, dots, king. $\{B,R\}$ can be the set of events that indicate Red or Black.