DAY 2 OF CHAPTER 13
NOW LET’S THINK ABOUT FAMILIES WITH 3 CHILDREN
A) CREATE A SAMPLE SPACE OF EQUALLY LIKELY OUTCOMES
B) WHAT’S THE PROBABILITY A 3-CHILD FAMILY HAS AT LEAST
ONE GIRL?
C) WHAT’S THE PROBABILITY THAT THERE ARE BOTH BOYS
AND GIRLS IN THE FAMILY?
NOW LET’S THINK ABOUT FAMILIES WITH 3 CHILDREN
A) CREATE A SAMPLE SPACE OF EQUALLY LIKELY OUTCOMES
B) WHAT’S THE PROBABILITY A 3-CHILD FAMILY HAS AT LEAST
ONE GIRL?
C) WHAT’S THE PROBABILITY THAT THERE ARE BOTH BOYS
AND GIRLS IN THE FAMILY?
COLORADO LICENSE PLATES CONSIST OF
3 DIGITS AND THEN 3 LETTERS.
HOW MANY DIFFERENT LICENSE PLATES ARE AVAILABLE?
COLORADO LICENSE PLATES CONSIST OF
3 DIGITS AND THEN 3 LETTERS.
HOW MANY DIFFERENT LICENSE PLATES ARE AVAILABLE?
ONE COMMON PROPOSAL FOR BEATING THE LOTTERY IS
TO NOTE WHICH NUMBERS HAVE COME UP LATELY,
ELIMINATE THOSE FROM CONSIDERATION, AND BET ON
NUMBERS THAT HAVE NOT COME UP FOR A LONG TIME.
EXPLAIN WHY THIS IS FAULTY REASONING AND WHAT THIS
IS REFERRED TO IN STATISTICS.
THE
LAW OF AVERAGES IS FALSE.
THE RANDOM METHODS FOR SELECTING LOTTERY NUMBERS
HAVE NO MEMORY OF PREVIOUS PICKS, SO THERE IS NO
CHANGE IN THE PROBABILITY THAT A CERTAIN NUMBER
WILL COME UP.
PASSWORDS
IN EACH OF THESE SITUATIONS, HOW MANY DIFFERENT
PASSWORDS ARE THERE?
A) THE ACCESS CODE FOR AN ATM IS 4 DIGITS ( LIKE 3551)
PASSWORDS
A) THE ACCESS CODE FOR AN ATM IS 4 DIGITS
PASSWORDS
IN EACH OF THESE SITUATIONS, HOW MANY DIFFERENT
PASSWORDS ARE THERE?
B) THE LOGIN CODE FOR AN EMAIL SITE IS 5 CHARACTERS,
ALTERNATING LETTER-DIGIT-LETTER-DIGIT-LETTER ( R5T6Y)
PASSWORDS
B) THE LOGIN CODE FOR AN EMAIL SITE IS 5 CHARACTERS,
ALTERNATING LETTER-DIGIT-LETTER-DIGIT-LETTER ( R5T6Y)
PASSWORDS
IN EACH OF THESE SITUATIONS, HOW MANY DIFFERENT
PASSWORDS ARE THERE?
C) THE EMAIL LOGIN CODE CAN ALTERNATE LETTERS AND
DIGITS WITH EITHER A LETTER OR DIGIT FIRST ( A7R3W OR
8M7T6)
PASSWORDS
C) THE EMAIL LOGIN CODE CAN
ALTERNATE LETTERS AND DIGITS WITH
EITHER A LETTER OR DIGIT FIRST
( A7R3W OR 8M7T6)
PASSWORDS
IN EACH OF THESE SITUATIONS, HOW MANY DIFFERENT
PASSWORDS ARE THERE?
D) THE EMAIL LOGIN CODE CAN BE ANY
MIXTURE OF LETTERS AND DIGITS IN
ANY ORDER, AND IS CASE SENSITIVE.
PASSWORDS
D) THE EMAIL LOGIN CODE CAN BE ANY MIXTURE OF LETTERS
AND DIGITS IN ANY ORDER, AND IS CASE SENSITIVE
PERMUTATIONS
JUST A
BIG WORD FOR “ORDERS” OR
“ARRANGEMENTS”
THE FORMULA FOR A
PERMUTATION IS
THERE ARE 8 RUNNERS IN A RACE TO DETERMINE
WHO ADVANCES TO STATE CHAMPIONSHIPS.
IN HOW MANY DIFFERENT ORDERS CAN THE
RUNNERS CROSS THE FINISH LINE?
THERE ARE 8 RUNNERS IN A RACE TO DETERMINE
WHO ADVANCES TO STATE CHAMPIONSHIPS.
IN HOW MANY DIFFERENT ORDERS CAN THE
RUNNERS CROSS THE FINISH LINE?
AT A TRACK MEET WE TYPICALLY DON’T CARE ABOUT THE
ENTIRE ORDER OF RUNNERS BUT REALLY JUST WHO COMES
IN 1ST, 2ND AND 3RD PLACES.
HOW MANY DIFFERENT WAYS CAN WE ORDER THE TOP
THREE OF 8 RUNNERS?
AT A TRACK MEET WE TYPICALLY DON’T CARE ABOUT THE
ENTIRE ORDER OF RUNNERS BUT REALLY JUST WHO COMES
IN 1ST, 2ND AND 3RD PLACES.
HOW MANY DIFFERENT WAYS CAN WE ORDER THE TOP
THREE OF 8 RUNNERS?
TRY EVALUATING SOME OF THESE FACTORIALS:
A) 4!
B)
C)
𝟓!
𝟑!
𝟏𝟎!
𝟒!𝟔!
TRY EVALUATING SOME OF THESE FACTORIALS:
A) 4! =
B)
𝟓!
𝟑!
C)
𝟏𝟎!
𝟒!𝟔!
=
YOU JUST DOWNLOADED 5 NEW ALBUMS
TO YOUR I-POD, AND ARE EAGER TO
LISTEN TO THEM.
HOW MANY DIFFERENT ORDERS CAN YOU
PLAY THEM IN?
YOU JUST DOWNLOADED 5 NEW ALBUMS
TO YOUR I-POD, AND ARE EAGER TO
LISTEN TO THEM.
HOW MANY DIFFERENT ORDERS CAN YOU
PLAY THEM IN?
YOU TAKE YOUR I-POD TO THE BEACH AND SELECT A
PLAYLIST OF YOUR 8 FAVORITE ALBUMS TO BE PLAYED IN
RANDOM ORDER. YOU’LL BE THERE LONG ENOUGH TO HEAR
5 OF THEM.
HOW MANY DIFFERENT ORDERS OF ALBUMS COULD YOU GET
TO LISTEN TO?
YOU TAKE YOUR I-POD TO THE BEACH
AND SELECT A PLAYLIST OF YOUR 8
FAVORITE ALBUMS TO BE PLAYED IN
RANDOM ORDER. YOU’LL BE THERE LONG
ENOUGH TO HEAR 5 OF THEM.
HOW MANY DIFFERENT ORDERS OF
ALBUMS COULD YOU GET TO LISTEN TO?
COMBINATIONS
WHEN WE DON’T CARE ABOUT WHAT ORDER
THINGS ARE, JUST THAT THEY ARE PART OF THE
GROUP!
THE BETTING SLIPS FOR NEW JERSEY’S PICK 6 LOTTO GAME
OFFER A FIELD OF NUMBERS FROM 1 TO 49.
EACH BETTER CAN CHOOSE 6 OF THEM.
YOU WIN THE GRAND PRIZE IF YOUR 6 NUMBERS MATCH
THOSE RANDOMLY CHOSEN ON TV BY THE NJ LOTTERY.
HOW MANY DIFFERENT SELECTIONS ARE POSSIBLE?
THE BETTING SLIPS FOR NEW JERSEY’S PICK 6 LOTTO GAME
OFFER A FIELD OF NUMBERS FROM 1 TO 49.
EACH BETTER CAN CHOOSE 6 OF THEM.
YOU WIN THE GRAND PRIZE IF YOUR 6 NUMBERS MATCH
THOSE RANDOMLY CHOSEN ON TV BY THE NJ LOTTERY.
HOW MANY DIFFERENT SELECTIONS ARE POSSIBLE?
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY 13-CARD BRIDGE HANDS CAN BE DEALT
FROM A DECK OF CARDS?
PERMUTATION OR COMBINATION
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY 13-CARD BRIDGE HANDS CAN BE DEALT
FROM A DECK OF CARDS?
PERMUTATION OR COMBINATION
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY 3-TURN COMBINATIONS COULD A PADLOCK
HAVE IF THERE ARE 60 NUMBERS ON THE DIAL AND
COMBINATIONS CAN’T HAVE REPEATED NUMBERS?
PERMUTATION OR COMBINATION
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY 3-TURN COMBINATIONS COULD A PADLOCK
HAVE IF THERE ARE 60 NUMBERS ON THE DIAL AND
COMBINATIONS CAN’T HAVE REPEATED NUMBERS?
PERMUTATION OR COMBINATION
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY BATTING ORDERS COULD A BASEBALL
MANAGER CREATE USING THE 9 PLAYERS IN HIS
STARTING LINEUP?
PERMUTATION OR COMBINATION
ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS?
A) HOW MANY BATTING ORDERS COULD A BASEBALL
MANAGER CREATE USING THE 9 PLAYERS IN HIS
STARTING LINEUP?
PERMUTATION OR COMBINATION
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
A) 4 JUNIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
A) 4 JUNIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
B) 4 SENIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
B) 4 SENIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
C) 2 JUNIORS AND 2 SENIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
C) 2 JUNIORS AND 2 SENIORS?
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
D) 2 OR 3 SENIORS? ( AND THE REST JUNIORS)
A HIGH SCHOOL VARSITY CLUB CONSISTS OF 13 ELECTED
REPRESENTATIVES, 8 SENIORS AND 5 JUNIORS.
THEY ARE SETTING UP A 4 – PERSON COMMITTEE TO PLAN
HOMECOMING.
HOW MANY DIFFERENT COMMITTEES BE FORMED IF THE
GROUP WILL CONSIST OF:
D) 2 OR 3 SENIORS? ( AND THE REST JUNIORS)