2. DAY 2 OF CHAPTER 13

3. 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?

5. COLORADO LICENSE PLATES CONSIST OF 3 DIGITS AND THEN 3 LETTERS. HOW MANY DIFFERENT LICENSE PLATES ARE AVAILABLE?

7. 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.

8. 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.

9. PASSWORDS IN EACH OF THESE SITUATIONS, HOW MANY DIFFERENT PASSWORDS ARE THERE? A) THE ACCESS CODE FOR AN ATM IS 4 DIGITS ( LIKE 3551)

10. PASSWORDS A) THE ACCESS CODE FOR AN ATM IS 4 DIGITS

11. 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)

12. PASSWORDS B) THE LOGIN CODE FOR AN EMAIL SITE IS 5 CHARACTERS, ALTERNATING LETTER-DIGIT-LETTER-DIGIT-LETTER ( R5T6Y)

13. 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)

14. PASSWORDS C) THE EMAIL LOGIN CODE CAN ALTERNATE LETTERS AND DIGITS WITH EITHER A LETTER OR DIGIT FIRST ( A7R3W OR 8M7T6)

15. 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.

16. PASSWORDS D) THE EMAIL LOGIN CODE CAN BE ANY MIXTURE OF LETTERS AND DIGITS IN ANY ORDER, AND IS CASE SENSITIVE

17. PERMUTATIONS JUST A BIG WORD FOR “ORDERS” OR “ARRANGEMENTS”

18. THE FORMULA FOR A PERMUTATION IS

19. 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?

23. AT A TRACK MEET WE TYPICALLY DON’T CARE ABOUT THE ENTIRE ORDER OF RUNNERS BUT REALLY JUST WHO COMES IN 1 ST, 2 ND AND 3 RD PLACES. HOW MANY DIFFERENT WAYS CAN WE ORDER THE TOP THREE OF 8 RUNNERS?

27. 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?

29. 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?

31. COMBINATIONS WHEN WE DON’T CARE ABOUT WHAT ORDER THINGS ARE, JUST THAT THEY ARE PART OF THE GROUP!

33. 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?

35. ARE THE FOLLOWING PERMUTATIONS OR COMBINATIONS? A) HOW MANY 13-CARD BRIDGE HANDS CAN BE DEALT FROM A DECK OF CARDS? PERMUTATION OR COMBINATION

37. 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

39. 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

41. 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?

43. 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?

45. 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?

47. 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)