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!