- WELCOME TO TWO EXAMPLES OF DETERMINING THE PROBABILITY
OF THE COMPLEMENT OF AN EVENT.
THE PROBABILITY THAT AN EVENT "A" WILL NOT OCCUR
IS CALLED THE COMPLEMENT OF EVENT "A."
NOW WE CAN SAY THE PROBABILITY THAT "A" WILL NOT OCCUR
IS EQUAL TO 1 - THE PROBABILITY THAT "A" WILL OCCUR.
LET'S LOOK AT AN EXAMPLE.
ONE CARD IS SELECTED FROM A DECK OF PLAYING CARDS.
WHAT IS THE PROBABILITY THE CARD IS NOT A DIAMOND?
THE PROBABILITY THAT THE CARD IS NOT A DIAMOND
MUST BE EQUAL TO 1
- THE PROBABILITY THAT THE CARD IS A DIAMOND.
HERE'S A PICTURE OF A DECK OF PLAYING CARDS.
THERE ARE A TOTAL OF 52 CARDS.
AND THERE ARE A TOTAL OF 13 DIAMONDS
WHICH MEANS THE PROBABILITY THE CARD IS NOT A DIAMOND
MUST BE EQUAL TO 1 OR 1/1
- THE PROBABILITY THAT THE CARD IS A DIAMOND
WHICH WOULD BE 13 OUT OF 52.
AGAIN THERE ARE A TOTAL OF 13 CARDS THAT ARE DIAMONDS.
LET'S GO AHEAD AND FIND THIS DIFFERENCE.
THE COMMON DENOMINATOR WOULD BE 52
SO MULTIPLY BOTH THE NUMERATOR AND DENOMINATOR BY 52.
SO THE DENOMINATOR STAYS 52,
THE NUMERATOR WOULD BE 52 - 13 WHICH = 39.
SO THE PROBABILITY THAT THE CARD IS NOT A DIAMOND
WOULD BE 39 DIVIDED BY 52.
NOTICE HOW THAT WOULD BE 39 CARDS THAT ARE NOT DIAMONDS.
NOW THIS DOES SIMPLIFY.
THERE'S A COMMON FACTOR OF 13. THIS SIMPLIFIES NICELY TO 3/4.
HOPEFULLY THIS MAKES SENSE.
WE CAN SEE THERE ARE FOUR ROWS OF 13,
3/4 OF THE CARDS ARE NOT DIAMONDS.
AND SINCE PROBABILITY CAN BE EXPRESSED AS A FRACTION,
DECIMAL OR PERCENTAGE,
LET'S GO AHEAD AND WRITE THIS AS A DECIMAL.
3 DIVIDED BY 4 = 0.75, CONVERT THIS TO A PERCENTAGE,
WE MULTIPLY BY 100, ADD A PERCENT SYMBOL,
REMOVE THE DECIMAL POINT TO THE RIGHT TWO PLACES
THIS WOULD BE 75%.
LET'S GO AHEAD AND TAKE A LOOK AT A SECOND EXAMPLE.
TWENTY PING PONG BALLS ARE NUMBERED FROM ONE TO 20.
WHAT IS THE PROBABILITY OF SELECTING ONE BALL
AND IT IS NOT GREATER THAN 17?
WELL THE PROBABILITY THAT THE BALL IS NOT GREATER THAN 17
MUST BE EQUAL TO 1
- THE PROBABILITY THAT THE BALL IS GREATER THAN 17.
SO LOOKING AT THE BALLS,
LET'S DETERMINE HOW MANY OF THEM ARE GREATER THAN 17.
WELL 17 IS NOT GREATER THAN 17 BUT 18, 19 AND 20 ARE.
SO THERE WOULD BE THREE BALLS OUT OF 20
THAT ARE GREATER THAN 17
WHICH MEANS THE PROBABILITY THE BALL IS NOT GREATER THAN 17
MUST BE EQUAL TO 1
OR 1/1 - THE PROBABILITY OF THE BALL BEING GREATER THAN 17.
THERE ARE THREE BALLS GREATER THAN 17 OUT OF 20.
SO 3/20 WOULD BE THE PROBABILITY THE BALL IS GREATER THAN 17.
LET'S GO AHEAD AND SUBTRACT, COMMON DENOMINATOR IS 20,
SO WE HAVE 20 - 3 WHICH IS 17,
17 DIVIDED BY 20 IS ALSO EQUAL TO 0.85
WHICH IS ALSO EQUAL TO 85%.
AGAIN 17 DIVIDED BY 20 = 0.85. IF WE WANT WE CAN VERIFY THIS.
AND THERE IT IS.
REMEMBER THE ORIGINAL PROBABILITY WAS THE PROBABILITY
THAT THE BALL IS NOT GREATER THAN 17
WHICH WOULD BE THE SAME AS SAYING IT'S LESS THAN
OR EQUAL TO 17.
SO IF WE GO BACK AND TAKE A LOOK AT THE LISTING FROM ONE TO 20,
NOTICE THERE ARE 17 NUMBERS THAT ARE NOT GREATER THAN 17.
THE NUMBERS 1, ALL THE WAY THROUGH 17,
GIVING US A PROBABILITY OF 17/20.
I HOPE YOU FOUND THESE TWO EXAMPLES HELPFUL.
THANK YOU FOR WATCHING.