Question

Look for the probability for an experiment of which requires you to select one card from a standard deck of 52 playing cards. Write your final answer as a fraction in the simplest form of a/b.

1.) P(the card is not a face)
2.) P(the card is a king)
3.) P(the sum is at least 7)
4.) P(the sum is at least 7)

Answer 1

In a deck of cards, there are
4 different card suits (Hearts, Diamonds, Spades, Clubs)
13 cards in each suit
3 face cards (Jack, Queen, King) in each suit, so 12 face cards total
10 cards which are not face cards, so 40 cards total with no face

1.
P(card is not face) = 40/52

2.
P(card is King) = 4/52

3.
Well if you're going to choose only one card (as stated in the problem) with sum at least 7, the card you'll pick must be from card 7 to 10 in any suit. That's 4 cards in each suit (cards 7, 8, 9, 10), and 4 cards x 4 suits = 16 cards total. So,
P(sum is at least 7) = 16/52
I'm actually not sure about this last one.

Just write them in simplest form.