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- GIVING A TEST TO A GROUP OF STUDENTS,
THE GRADES AND GENDER ARE SUMMARIZED BELOW.
IF ONE STUDENT WAS CHOSEN AT RANDOM,
FIND THE PROBABILITY THAT THE STUDENT GOT AN "A."
SO WE WANT TO FIND THE PROBABILITY
THAT A RANDOM STUDENT RECEIVED AN "A."
LOOKING AT THE TABLE, NOTICE HOW THIS COLUMN HERE
TELLS US THE NUMBER OF "A" STUDENTS.
THERE WERE A TOTAL OF 30 "A" STUDENTS,
13 OF WHICH WERE MALE, 17 OF WHICH WERE FEMALE.
AND LOOKING AT THE TOTALS COLUMN,
NOTICE 31 MALES TOOK THE TEST, 37 FEMALES TOOK THE TEST.
THEREFORE, THERE WERE A TOTAL OF 68 TEST TAKERS.
SO OF THE 68 TEST TAKERS, 30 RECEIVED "A's,"
AND THEREFORE THE PROBABILITY THAT A STUDENT CHOSEN AT RANDOM
WOULD HAVE GOTTEN AN "A" WOULD BE
THE NUMBER OF STUDENTS RECEIVING AN "A," WHICH IS 30,
DIVIDED BY THE NUMBER OF STUDENTS THAT TOOK THE TEST,
WHICH IS 68.
SO THIS IS THE PROBABILITY,
BUT WE ARE ASKED TO EXPRESS THE PROBABILITY
AS A FRACTION OR A DECIMAL.
IF WE DO EXPRESS IT AS A FRACTION,
WE DO WANT TO MAKE SURE THAT A FRACTION IS IN SIMPLIFIED FORM.
NOTICE 30 AND 68 DO SHARE A COMMON FACTOR OF 2
AND THEREFORE AS A FRACTION
THE PROBABILITY OF AN "A" WOULD BE 15/34.
THIS FRACTION IS IN SIMPLIFIED FORM.
LET'S ALSO GIVE THE PROBABILITY AS A DECIMAL,
AND EVEN THOUGH IT DOESN'T ASK, AS A PERCENTAGE.
SO TO CONVERT THE FRACTION TO A DECIMAL WE'LL DIVIDE.
SO 15 DIVIDED BY 34.
LET'S ROUND THIS TO 4 DECIMAL PLACES,
SO THIS WOULD BE APPROXIMATELY 0.4412.
NOTICE HOW THE 7 INDICATES TO ROUND UP.
SO THE DECIMAL VALUE IS GOING TO BE AN APPROXIMATION, 0.4412.
LET'S ALSO WRITE THIS AS A PERCENTAGE.
TO CONVERT A DECIMAL TO A PERCENTAGE WE MULTIPLY BY 100
AND ADD A PERCENT SIGN
OR MOVE THE DECIMAL POINT TO THE RIGHT 2 TIMES,
SO THIS WOULD BE 44.12%.
BUT IT IS IMPORTANT TO KEEP IN MIND
THAT THE FRACTION IS THE EXACT PROBABILITY,
AND THE DECIMAL AND PERCENT ARE ROUNDED APPROXIMATIONS.
I HOPE YOU FOUND THIS HELPFUL.