Probability & Statistics For 4th Grade Math Club Cherry Crest Elementary School Bellevue, WA Oct. 28, 2014

What is Probability? 0<=Possibility <= 1 The extent to which an event is likely to occur. Measured by the ratio of the favorable cases to the whole number of cases possible. Ricky wants to play video game in the Morning Probability = 0, Impossible Event (sun rising in the west) Ricky wants to have some vegetables for dinner Probability = 0.5 May or may not Ricky wants to do his math homework tonight Probability = 1, Sure Event Yes! You can have as much as you like! (sun rising in the east) 0 <=Probability <=1 0<=Possibility <= 1

P(A)= 𝑁(𝐴) 𝑁(𝑆) N(A) − Number of possibilities that meet the condition 𝑁 𝑆 − Number of equally likely possibilities vs P(Deer to Win) = 1/2 ? Condition P(A) Head 𝟏/𝟐 Tail Condition P(A) Get 3 1/𝟔 Not equally Likely

What exactly does probability mean???? Throw a dice 6 𝑡𝑖𝑚𝑒𝑠⇒ expect to get 1 time of ‘3’. Throw a dice 30 𝑡𝑖𝑚𝑒𝑠⇒ expect to get 5 times of ‘3’. Throw a dice 600 𝑡𝑖𝑚𝑒𝑠⇒ expect to get 100 times of ‘3’. The more times your throw, the results => the probability Condition P(A) Get 3 1/𝟔

P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 52 cards, 4 suits Red: Hearts and Diamonds Black: Clubs and Spades 13 cards: A.2.3.4.5.6.7,8,9,10,J.Q.K Condition P(A) Head 𝟏/𝟐 Tail Condition P(A) 2 𝟏/𝟔 3 or 4 𝟐/𝟔 = 1/3 odd 3/6 = 1/2 Condition P(A) Hearts 𝟏𝟑/𝟓𝟐 = ¼ Red 26/𝟓𝟐 = ½ Jacks 4/52 = 1/13 P(head) + P(tail) = 1 P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 1 𝑃(𝑜𝑛𝑒 𝑐𝑎𝑟𝑑) = 1 Sum of all possibilities of one event = 1 0<=Possibility <= 1

Question #1 (2013 AMC8 question #8)   P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 1. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 ? 2. 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 ?

Question #1 (2013 AMC8 question #8) Outcome => 2 Cons heads 3 heads Heads > Tails HHH Yes HHT No HTH THH TTH TTT THT HTT 3 1 4 1. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 ? 2. 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 ? 1. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 =3 2. 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 = 8 𝑂𝑟: 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 = 2x2x2

Question #2 (2013 AMC8 question #14) Abe and Bean each randomly picks a jelly bean to show the other. What is probability that the color match? Abe Bean P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 1. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 ? 2. 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 = 4, 6, or 8? 𝟑/8

Question #3 (2007 AMC8 question #21) Two cards are dealt from a deck of four red card labeled A, B, C, and D and four green cards labeled A, B, C, D. A winning pair is two of the same color or two of the same letter. What is the probability of drawing a winning pair? P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 A A B B 2. 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 ? 7x8/2 = 28 C C 1. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 ? 4x3/2x2 + 4 = 16 D D

Statistics Mean, Median, Mode, Range {2, 2, 6, 9, 3, 4, 5} Mean: average (2+2+6+9+3+4+5)/7 = 31/7 Mode: Most common number {2, 2, 3, 4, 5, 6, 9} 2 could have more than one mode Median: the middle value when all values in order {2, 2, 3, 4, 5, 6, 9} 4 or average of two numbers Range: difference between lowest and highest 9- 2 = 7

Question #4 (2012 AMC8 question #7) Isabella takes 4 100-points tests. Her goal is to achieve average of 95. Her first two test scores were 97 and 91. To reach her goal, what is the lowest possible score she could have made on the third test? 97 + 91 + + = 95x4 lowest highest =100 x = 95x4 – 97 -91 – 100 = 92

Question #5 (2012 AMC8 question #11) The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and x are all equal. What is the value of x? 3, 4, 5, 6, 6, 7 Two possible medians (3+4+5+6+6+7+x)/7 = 5 or 6 31+x = 5x7 or 31 + x = 6x7 x= 4 or x = 11 , which one is the right answer?

Question #6 (2012 AMC8 question #22) Let R be a set of nine distinct integers. Six of the elements are 2, 3, 4, 6, 9, and 14. What is the number of possible values of the median of R? A. 4, B. 5, C. 6, D.7, E. 8 2, 3, 4, 6, 9, 14 -2, -1, 0, 2, 3, 4, 6, 9, 14 -2, 0, 2, 3, 4, 6, 9, 14, 15 D.7

Tests 10 mintues

Summary Sum of all possibilities of one event = 1 0<=Possibility <= 1 P(A)= 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 𝑚𝑒𝑒𝑡𝑠 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡ℎ𝑖𝑛𝑔𝑠 Mean, Median, Mode, Range Math is Fun!