- A FAIR DIE IS ROLLED.
WE WANT TO FIND THE PROBABILITY OF THE EVENTS GIVEN HERE BELOW.
BEFORE WE DO THIS THOUGH,
LET'S CONSIDER THE SAMPLE SPACE OR THE POSSIBLE OUTCOMES
WHEN ROLLING A FAIR DIE PICTURED HERE ON THE RIGHT.
THE DIE HAS SIX SIDES NUMBERED 1 THROUGH 6,
AND THEREFORE THE SAMPLE SPACE OR POSSIBLE OUTCOMES
WOULD BE 1, 2, 3, 4, AND 6.
SO WE'RE CONSIDERING THE PROBABILITY OF AN EVENT
WHICH IS EQUAL TO THE FAVORABLE NUMBER OF OUTCOMES
DIVIDED BY THE TOTAL NUMBER OF OUTCOMES.
THE TOTAL NUMBER OF OUTCOMES WILL ALWAYS BE SIX,
AS WE SEE HERE.
SO FOR PART "A," WE'RE GOING TO DETERMINE THE PROBABILITY
THAT THE NUMBER SHOWING IS A 5 WHICH WE CAN WRITE LIKE THIS.
NOTICE HOW FROM THE SAMPLE SPACE WE CAN SEE
THERE'S ONLY 1 FAVORABLE OUTCOME GIVEN HERE BY THE NUMBER 5,
AND THEREFORE THE PROBABILITY OF ROLLING A 5
WOULD BE 1 DIVIDED BY 6 OR 1/6.
PROBABILITY CAN BE EXPRESSED
AS A FRACTION, DECIMAL, OR PERCENTAGE,
SO LET'S GIVE ALL THREE FORMS OF THE PROBABILITY.
TO CONVERT THE FRACTION TO A DECIMAL,
WE WOULD DIVIDE 1 DIVIDED BY 6.
1/6 = 0.16 WITH THE 6 REPEATING,
SO THE EXACT FORM OF THE DECIMAL WOULD BE 0.16
WITH A BAR OVER THE 6.
TO CONVERT THE DECIMAL TO A PERCENTAGE WE MULTIPLY BY 100,
ADD A PERCENT SIGN WHICH WOULD GIVE US,
NOTICE AGAIN THE 6 IS REPEATING, SO WE'D HAVE 16.6 REPEATING %.
WE CAN ALSO MOVE THE DECIMAL TO THE RIGHT TWO PLACES
AND ADD A PERCENT SIGN.
NEXT, WE WANT TO DETERMINE THE PROBABILITY
THE NUMBER SHOWING IS AN EVEN NUMBER.
EVEN NUMBERS ARE DIVISIBLE BY 2,
SO AGAIN, LOOKING AT OUR SAMPLE SPACE
WE HAVE 3 FAVORABLE OUTCOMES, THE 2, 4, OR 6.
AND THEREFORE THE PROBABILITY OF ROLLING AN EVEN NUMBER
WOULD BE EQUAL TO 3, 6, OR 3 DIVIDED BY 6
WHICH DOES SIMPLIFY TO 1/2,
WHICH WE SHOULD RECOGNIZE AS A DECIMAL AS 0.5
AND AS A PERCENTAGE, 50%.
AND THEN FINALLY, WE WANT TO DETERMINE THE PROBABILITY
THE NUMBER SHOWING IS GREATER THAN 2.
WE NEED TO BE A LITTLE CAREFUL HERE.
NOTICE 2 IS NOT GREATER THAN 2,
SO THE FAVORABLE OUTCOMES WOULD BE 3, 4, 5, AND 6.
SO THERE ARE FOUR FAVORABLE OUTCOMES
OUT OF SIX TOTAL OUTCOMES,
AND THEREFORE THE PROBABILITY OF THE NUMBER BEING GREATER THAN 2
= 4/6 WHICH SIMPLIFIES TO 2/3.
WE SHOULD RECOGNIZE THIS AS 0.6 REPEATING,
BUT LET'S GO AHEAD AND VERIFY THAT.
2 DIVIDED BY 3 = 0.6 REPEATING.
SO AS A DECIMAL WE WOULD HAVE 0.6 WITH A BAR OVER THE 6
SHOWING THE 6 REPEATS,
AND AS A PERCENTAGE WE WOULD HAVE 66.6 REPEATING %.
NOTICE HOW IF WE GO BACK TO THE CALCULATOR JUST FOR A MOMENT,
WE MULTIPLY THIS BY 100,
IT DOES CONVERT THE DECIMAL TO A PERCENT.
WE JUST HAVE TO REMEMBER TO ADD THE PERCENT SIGN.
WE ALSO NEED TO RECOGNIZE THE 6 IS REPEATING
EVEN THOUGH THE CALCULATOR IS ROUNDING HERE ON THE FAR RIGHT.
SO HERE WE EXPRESSED EACH PROBABILITY AS A FRACTION,
DECIMAL, AND PERCENTAGE.
JUST BE SURE IF YOUR QUESTION INDICATES, YOU KNOW,
THE PROBABILITY IN A SPECIFIC WAY, YOU DO SO.
I HOPE THIS WAS HELPFUL.