There are 52 cards in a standard deck (discounting Jokers), so the probability of drawing a card is defined as (number of possible cards)/52:
a) there are 4 queens, so the probability of drawing a queen is 4/52 or 1/13
b) there are 13 hearts, so 13/52 or 1/4
c) there are 12 face cards, so 12/52 or 3/13
d) there are 8 cards in each suit > 5 (6,7,8,9,10,J,Q,K) and 4 suits, so 32 possible cards; 32/52 = 8/13
To find the odds of NOT drawing these cards, simply subtract the odds of drawing them from 1:
a) 1 - 1/13 = 12/13