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- A CARD IS DRAWN RANDOMLY FROM A STANDARD 52-CARD DECK.
FIND THE PROBABILITY OF THE GIVEN EVENT.
AND WE HAVE THREE PROBABILITIES TO FIND.
BEFORE WE BEGIN,
LET'S DESCRIBE THE STANDARD DECK OF CARDS GIVEN HERE.
AGAIN WE HAVE 52 CARDS, THERE ARE 4 SUITS GIVEN IN THE ROWS.
WE HAVE THE SPADES, THE DIAMONDS, THE CLUBS,
AND THE HEARTS AND THERE ARE 13 RANKS OR 13 TYPES OF CARDS.
WE HAVE THE 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, AND 10s.
THEN WE HAVE THE FACE CARDS, WHICH ARE THE JACKS,
QUEENS, AND KINGS AND FINALLY WE HAVE THE ACES.
SO FOR PART "A,"
WE WANT TO FIND THE PROBABILITY THAT A CARD WOULD BE A 2.
SO THE PROBABILITY IF WE SELECT ONE CARD AND IT'S A 2
IS EQUAL TO THE NUMBER OF 2s DIVIDED BY THE NUMBER OF CARDS.
SO LOOKING AT OUR DECK, HERE ARE THE 2s.
THERE'S ONE 2 OF EACH SUIT OR A TOTAL OF FOUR 2s.
SO THE PROBABILITY OF SELECTING A 2 WOULD BE 4/52
OR 4 DIVIDED BY 52 WHICH DOES SIMPLIFY.
THERE'S A COMMON FACTOR OF 4 HERE.
SO THE EXACT PROBABILITY AS A FRACTION WOULD BE 1/13.
LET'S ALSO CONVERT TO A DECIMAL AND A PERCENT.
TO DO THIS WE'LL DIVIDE,
1 DIVIDED BY 13 = APPROXIMATELY 0.0769,
WHICH AS A PERCENT WOULD BE 7.69%.
TO CONVERT A DECIMAL TO A PERCENT,
WE MULTIPLY IT BY 100 AND ADD A PERCENT SIGN
MOVING THE DECIMAL POINT TO THE RIGHT TWO PLACES.
NEXT WE WANT TO DETERMINE THE PROBABILITY
THAT THE CARD IS A FACE CARD,
MEANING IT'S A JACK, QUEEN, OF KING.
SO THE PROBABILITY OF A FACE CARD,
WOULD BE EQUAL TO THE NUMBER OF FACE CARDS
DIVIDED BY THE TOTAL NUMBER OF CARDS.
AGAIN, THE FACE CARDS ARE HERE THE JACKS, QUEENS, AND KINGS.
THERE ARE 12 FACE CARDS SO THE PROBABILITY OF A FACE CARD
WOULD BE 12 DIVIDED BY 52.
AGAIN THIS SIMPLIFIES, COMMON FACTOR OF 4.
SO THIS WOULD BE 3/13 AS EXACT PROBABILITY.
AGAIN, LET'S CONVERT TO A DECIMAL AND A PERCENT.
SO 3 DIVIDED BY 13 WOULD BE APPROXIMATELY 0.2308.
NOTICE HOW THE 6 HERE INDICATES WE ROUND UP.
WHICH WOULD BE 23.08%.
AND NOW FOR OUR LAST PROBABILITY
WE CAN ACTUALLY DO THIS TWO WAYS.
WE WANT TO FIND THE PROBABILITY THAT THE CARD DRAWN
IS NOT A FACE CARD.
WE'LL FIRST USE JUST A BASIC PROBABILITY FORMULA.
SO THE PROBABILITY OF NOT A FACE CARD
WOULD BE EQUAL TO THE NUMBER OF NON-FACE CARDS
DIVIDED BY THE TOTAL NUMBER OF CARDS WHICH WE KNOW IS 52.
WELL IF THESE ARE THE FACE CARDS THEN THE REST OF THE CARDS
WOULD BE NON-FACE CARDS.
SO THE NON-FACE CARDS ARE THESE CARDS HERE,
AS WELL AS THOSE OVER HERE.
WELL, IF THERE ARE 52 CARDS AND 12 OF THEM ARE FACE CARDS,
52 - 12 LEAVES 40 NON-FACE CARDS.
SO THE PROBABILITY OF NOT A FACE CARD WOULD BE 40/52,
AND AGAIN, SIMPLIFYING.
COMMON FACTOR OF 4 GIVES US 10/13
WHICH AS A DECIMAL WOULD BE APPROXIMATELY 0.7692.
WHICH WOULD BE 76.92%.
BUT THE PROBABILITY OF NOT A FACE CARD
IS ACTUALLY THE PROBABILITY OF A COMPLIMENT.
WHEN WE HAVE A COMPLIMENT LIKE THIS
OR THE PROBABILITY OF NOT SOMETHING OCCURRING,
WE CAN WRITE THIS AS THE PROBABILITY
OF LET'S SAY F FOR FACE CARD,
WITH EITHER AN APOSTROPHE OR A BAR--LET'S USE A BAR.
THIS MEANS A PROBABILITY
OF NOT F WHICH IS EQUAL TO 1 - THE PROBABILITY OF F.
THIS IS TRUE BECAUSE WE KNOW
THE PROBABILITY OF SELECTING A FACE CARD
+ THE PROBABILITY OF NOT SELECTING A FACE CARD
WOULD BE EQUAL TO 1 OR 100%.
SO WE CAN USE THIS FORMULA TO FIND THE SAME PROBABILITY.
NOTICE HOW WE WOULD HAVE 1 - THE PROBABILITY OF A FACE CARD,
WHICH WE FOUND IN PART B AS 3/13.
WELL, 1 = 13/13,
13/13 - 3/13 GIVES US THE SAME RESULT OF 10/13,
WHICH WE FOUND USING THE BASIC PROBABILITY FORMULA.
I HOPE YOU FOUND THIS HELPFUL.