Explanation:
a probability is always the ratio
desired cases / totally possible cases
when pulling one card out of 52 cards, the totally possible cases for the result are 52.
now, all we need to do is "counting" or calculating the desired cases for each problem.
a 3 or a heart is pulled.
it is important to really read this carefully : 3 OR a heart. not 3 and a heart (that would ask for the probability to pull the 3 of hearts card, as no other card would satisfy the criteria).
we have 13 cards of heart.
and we have 4 cards of the value 3. but one of them is already included in the 13 cards of heart.
so, we need to add only 3 to these 13 and get 16 desired cards.
the probability is therefore
16/52 = 4/13 = 0.307692308... ≈ 0.308
a face card OR a club is pulled.
face cards are Jack, Queen and King (the ones with faces on the cards). so, 3 per suit, 4 suits = 12 cards.
we have 13 cards of club.
3 of these cards are already in the group of face cards, so we need to add only 10 to to this group for the desired cases. and the probability is
22/52 = 11/26 = 0.423076923... ≈ 0.423
a face card AND a heart is pulled.
we have 13 cards of heart.
and now it is AND to be a face card (not OR like in the previous question).
there are only 3 face cards of heart. the probability is
3/52 = 0.057692308... ≈ 0.058