Probability Underpins a Well-Prepared Mind
Statistics and Probability: A Challenging Discipline
FATE and FIGURES
(Chance Favors the Prepared Mind) Test your math prowess, beat the clock, and defy fate! π
How to Play:
- Answer statistics and probability challenges across 5 levels (Grade 7-11)
- Progress through levels by answering correctly
- Beat the timer: fastest time to Level 5 wins π
Are you prepared to challenge Fate and Figures? π
Play
Choose a Challenge
Click a Category to begin
πLevel 1
Statistics
π΅Level 3 Marble Mystery
π΅ Level 2 Sound Clash
βLevel 5 Final Challenge
ποΈ Level 4 Token Draw
30 seconds 2 attempts only
A group of grade 7 students recorded the number of books they read in one month. The numbers are: 6,8,10,8,12,4,8
πWhat is the MEAN of the data?
A. 6
B. 7
C. 8
D. 9
LAST CHANCE
A group of grade 7 students recorded the number of books they read in one month. The numbers are: 5,7,19,8,11,6,10 πWhat is the MEAN of the data?
A. 6
B. 7
C. 8
D. 9
ππCorrect !ππ
First, arrange the numbers in order:
5,6,7,8,9,11,10 Mean:
(5+6+7+8+9+10+11)=56
56/7 = 8
Median:
Middle number = 8
Mode:
Most common number = 8
Next
Out of tries !
Level 2 - Sound Clash
Only the sharpest will survive....
Play
30 seconds 2 attempts only
Sound Clash Showdown
In a class of 40 students: 19 students liked dancehall
The number who liked reggae was twice the number who liked soca
π How many student like Soca?
A. 5
B. 7
C. 10
D. 12
TRY AGAIN! LAST CHANCE
Sound Clash Showdown
In a class of 40 students: 19 students liked dancehall
The number who liked reggae was twice the number who liked soca
π How many student like Soca?
A. 5
REMEMBERβ¦
Start by finding how many students are left after dancehall.
Then use the relationship between Soca and Reggae.
B. 7
C. 10
D. 12
ππCorrect !ππ Let's break it down...
Step 1: Total students = 40
Step 2: Dancehall = 19
Step 3: Remaining students : 40-19 = 21
Step 4: Let Soca = x and Reggae = 2x Step 5: x+2x=21
3x=21
x=7
Final Answer: Soca: 7 Since reggae is twice Soca, Reggae = 14 β
Next
Out of tries!
Listen closely...patterns matter
π΅Level 3 - MARBLE MYSTERY
What are the chances...draw wisely
Play
30 seconds 2 attempts only
Marble Mystery Challenge
A bag contains red, blue, and green marbles - 12 red marbles represent β
of the total
- The probability of picking a blue marble is Β½
π How many green marbles are in the bag?
B. 6
A. 4
C. 8
D. 12
TRY AGAIN! LAST CHANCE
Marble Mystery Challenge
A bag contains red, blue, and green marbles - 12 red marbles represent β
of the total
- The probability of picking a blue marble is Β½
π How many green marbles are in the bag?
A. 4
B. 6
C. 8
D. 12
ππ FANTASTIC!ππ
Great job! The correct answer is 6 green marbles
How the Mystery Was Solved
Step 1:
12 represents β
of the total
Total marbles = 12 x 3 = 36
Step 2:
Blue marbles = Β½ of 36 = 18
Step 3:
Green marbles = 36-12-18 = 6
Next
Out of tries !
Level 4 - TOKEN DRAW
Play the odds... choose wisely
Play
Token Draw
30 seconds 2 attempts only
A box contains: 5 red tokens
3 blue tokens
4 green tokens
Two tokens are drawn without replacement.
π€Which is more likely?
B. One blue and one green
A. Both tokens are red
C. Both tokens are the same color
D. All outcomes are equally alike
TRY AGAIN! LAST CHANCE
Token Draw
A box contains: 5 red tokens
3 blue tokens
4 green tokens
Two tokens are drawn without replacement.
π€Which is more likely?
B. One blue and one green
A. Both tokens are red
C. Both tokens are the same color
D. All outcomes are equally alike
Correct ! You Chose the Best Outcome
Total Tokens: 5+3+4 =12
1. Both red: 5/12 Γ 4/11 = 5/33 2. One blue and one green:
(3/12 Γ 4/11) + (4/12 Γ 3/11) = 2/11
3. Compare:
2/11 = 6/33
5/33 < 6/33
Therefore, one blue and one green is more likely
Next
Out of tries !
Think about how many different combinations are possible.
Level 5 YOU MADE IT TO THE FINALE
Only the sharpest will survive....
Play
The Cumulative Quest
30 seconds 2 attempts only
A group of 40 students received the following marks (out of 60).
A. π
B. π
C. π
The Cumulative Quest
TRY AGAIN! LAST CHANCE
A group of 40 students received the following marks (out of 60).
A. π
B. π
C. π
CORRECT!
The median score is approximately 33.33
See solution
πSolution
How it was solved........
First, find the Median position
Median position: π‘ππ‘ππ ππ’ππππ2 ππ π£πππ’ππ = 402/ 2 =20
The 20th value lies in the 30β40 class (since cumulative frequency goes from 16 to 28).
Using linear interpolation formula or formula for finding median of grouped data:
Where:
πΏππΆπΉ= total frequency = 40 = lower class boundary of the median class = 30 = cumulative frequency before the median class = 16 π= frequency of the median class = 12
= class width = 10
Then, π now find the Median
So, Median = 30 +402 β16 x 10 12
= 30 + 2012β16 x 10
= 30 + 4 x 10 12
= 30 + 3.33
Median β 33.3 marks
Out of tries!
Hint: Find the middle value.40 students find the 20th. Try again!
GAME OVER
GAME OVER
Fate wasn't on your side this time...
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Transcript
Probability Underpins a Well-Prepared Mind Statistics and Probability: A Challenging Discipline
FATE and FIGURES
(Chance Favors the Prepared Mind) Test your math prowess, beat the clock, and defy fate! π How to Play: - Answer statistics and probability challenges across 5 levels (Grade 7-11) - Progress through levels by answering correctly - Beat the timer: fastest time to Level 5 wins π Are you prepared to challenge Fate and Figures? π
Play
Choose a Challenge
Click a Category to begin
πLevel 1 Statistics
π΅Level 3 Marble Mystery
π΅ Level 2 Sound Clash
βLevel 5 Final Challenge
ποΈ Level 4 Token Draw
30 seconds 2 attempts only
A group of grade 7 students recorded the number of books they read in one month. The numbers are: 6,8,10,8,12,4,8 πWhat is the MEAN of the data?
A. 6
B. 7
C. 8
D. 9
LAST CHANCE
A group of grade 7 students recorded the number of books they read in one month. The numbers are: 5,7,19,8,11,6,10 πWhat is the MEAN of the data?
A. 6
B. 7
C. 8
D. 9
ππCorrect !ππ
First, arrange the numbers in order: 5,6,7,8,9,11,10 Mean: (5+6+7+8+9+10+11)=56 56/7 = 8 Median: Middle number = 8 Mode: Most common number = 8
Next
Out of tries !
Level 2 - Sound Clash
Only the sharpest will survive....
Play
30 seconds 2 attempts only
Sound Clash Showdown
In a class of 40 students: 19 students liked dancehall The number who liked reggae was twice the number who liked soca π How many student like Soca?
A. 5
B. 7
C. 10
D. 12
TRY AGAIN! LAST CHANCE
Sound Clash Showdown
In a class of 40 students: 19 students liked dancehall The number who liked reggae was twice the number who liked soca π How many student like Soca?
A. 5
REMEMBER⦠Start by finding how many students are left after dancehall. Then use the relationship between Soca and Reggae.
B. 7
C. 10
D. 12
ππCorrect !ππ Let's break it down...
Step 1: Total students = 40 Step 2: Dancehall = 19 Step 3: Remaining students : 40-19 = 21 Step 4: Let Soca = x and Reggae = 2x Step 5: x+2x=21 3x=21 x=7
Final Answer: Soca: 7 Since reggae is twice Soca, Reggae = 14 β
Next
Out of tries!
Listen closely...patterns matter
π΅Level 3 - MARBLE MYSTERY
What are the chances...draw wisely
Play
30 seconds 2 attempts only
Marble Mystery Challenge
A bag contains red, blue, and green marbles
- 12 red marbles represent β
of the total
- The probability of picking a blue marble is Β½
π How many green marbles are in the bag?B. 6
A. 4
C. 8
D. 12
TRY AGAIN! LAST CHANCE
Marble Mystery Challenge
A bag contains red, blue, and green marbles
- 12 red marbles represent β
of the total
- The probability of picking a blue marble is Β½
π How many green marbles are in the bag?A. 4
B. 6
C. 8
D. 12
ππ FANTASTIC!ππ
Great job! The correct answer is 6 green marbles
How the Mystery Was Solved
Step 1: 12 represents β of the total Total marbles = 12 x 3 = 36 Step 2: Blue marbles = Β½ of 36 = 18 Step 3: Green marbles = 36-12-18 = 6
Next
Out of tries !
Level 4 - TOKEN DRAW
Play the odds... choose wisely
Play
Token Draw
30 seconds 2 attempts only
A box contains: 5 red tokens 3 blue tokens 4 green tokens Two tokens are drawn without replacement. π€Which is more likely?
B. One blue and one green
A. Both tokens are red
C. Both tokens are the same color
D. All outcomes are equally alike
TRY AGAIN! LAST CHANCE
Token Draw
A box contains: 5 red tokens 3 blue tokens 4 green tokens Two tokens are drawn without replacement. π€Which is more likely?
B. One blue and one green
A. Both tokens are red
C. Both tokens are the same color
D. All outcomes are equally alike
Correct ! You Chose the Best Outcome
Total Tokens: 5+3+4 =12 1. Both red: 5/12 Γ 4/11 = 5/33 2. One blue and one green: (3/12 Γ 4/11) + (4/12 Γ 3/11) = 2/11 3. Compare: 2/11 = 6/33 5/33 < 6/33 Therefore, one blue and one green is more likely
Next
Out of tries !
Think about how many different combinations are possible.
Level 5 YOU MADE IT TO THE FINALE
Only the sharpest will survive....
Play
The Cumulative Quest
30 seconds 2 attempts only
A group of 40 students received the following marks (out of 60).
A. π
B. π
C. π
The Cumulative Quest
TRY AGAIN! LAST CHANCE
A group of 40 students received the following marks (out of 60).
A. π
B. π
C. π
CORRECT!
The median score is approximately 33.33
See solution
πSolution
How it was solved........
First, find the Median position Median position: π‘ππ‘ππ ππ’ππππ2 ππ π£πππ’ππ = 402/ 2 =20 The 20th value lies in the 30β40 class (since cumulative frequency goes from 16 to 28). Using linear interpolation formula or formula for finding median of grouped data:
Where: πΏππΆπΉ= total frequency = 40 = lower class boundary of the median class = 30 = cumulative frequency before the median class = 16 π= frequency of the median class = 12 = class width = 10
Then, π now find the Median So, Median = 30 +402 β16 x 10 12 = 30 + 2012β16 x 10 = 30 + 4 x 10 12 = 30 + 3.33
Median β 33.3 marks
Out of tries!
Hint: Find the middle value.40 students find the 20th. Try again!
GAME OVER
GAME OVER
Fate wasn't on your side this time...