probability & statistics for 4 th grade math club cherry crest elementary school bellevue, wa...
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Probability & StatisticsFor 4th Grade Math Club
Cherry Crest Elementary School
Bellevue, WA
Oct. 28, 2014
What is Probability?• 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.
0 <=Probability <=1
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<=Possibility <= 1
P(A)
Condition P(A)
Get 3 1 Not equally Likely
P ( Deer to Win ) = 1/2 ?
vs
Condition P(A)
Head
Tail
Condition P(A)
Get 3 1
Texpect to get 1 time of ‘3’.What exactly does probability mean????
expect to get 100 times of ‘3’.expect to get 5 times of ‘3’.
The more times your throw, the results => the probability
P(A)
Condition P(A)
Head
Tail
Condition P(A)
2
3 or 4 = 1/3
odd 3/6 = 1/2
Sum of all possibilities of one event = 1P(head) + P(tail) = 1P(1)+P(2)+P(3)+P(4)+P(5)+P(6) = 1
Condition P(A)
Hearts = ¼
Red 26 = ½
Jacks 4/52 = 1/13
= 1
52 cards, 4 suitsRed: Hearts and DiamondsBlack: Clubs and Spades13 cards: A.2.3.4.5.6.7,8,9,10,J.Q.K
0<=Possibility <= 1
Question #1 (2013 AMC8 question #8)
P(A) ?
1.𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 h𝑡 𝑖𝑛𝑔𝑠𝑚𝑒𝑒𝑡𝑠𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠?
Question #1 (2013 AMC8 question #8)
?
1.𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 h𝑡 𝑖𝑛𝑔𝑠𝑚𝑒𝑒𝑡𝑠𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠?
= 8
1.𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 h𝑡 𝑖𝑛𝑔𝑠𝑚𝑒𝑒𝑡𝑠𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠=3
𝑂𝑟 : = 2x2x2
Outcome => 2 Cons heads
3 heads Heads > Tails
HHH Yes Yes Yes
HHT Yes No Yes
HTH No No Yes
THH Yes No Yes
TTH No No No
TTT No No No
THT No No No
HTT No No No
3 1 4
Question #2 (2013 AMC8 question #14)
P(A)Abe and Bean each randomly picks a jelly bean to show the other. What is probability that the color match?
Abe Bean
1.𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 h𝑡 𝑖𝑛𝑔𝑠𝑚𝑒𝑒𝑡𝑠𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠? = 4, 6, or 8?
8
Question #3 (2007 AMC8 question #21)
P(A)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?
A A
B
C
D
B
C
D
?
1.𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 h𝑡 𝑖𝑛𝑔𝑠𝑚𝑒𝑒𝑡𝑠𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠?
7x8/2 = 28
4x3/2x2 + 4 = 16
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
Statistics
{2, 2, 6, 9, 3, 4, 5}
Mean, Median, Mode, Range
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?
Two possible medians
(3+4+5+6+6+7+x)/7 = 5 or 6
3, 4, 5, 6, 6, 7
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 = 10<=Possibility <= 1P(A)
Mean, Median, Mode, Range
Math is Fun!