Probability Powerplay
Level 6, 2026-06-24
A Crazy Die has 5 sides, but each side has a different probability of being rolled. This is is the probability distribution of the sides being rolled:


0.90.1
12345
Number

What is the probability of rolling a number that is smaller than or equal to 2?
[1]
A wheel has 6 sections, each a number on it from 1 to 6. If you spin an odd number you win that amount of dollars, if you spin an even number you lose.
What prize do we expect to get if we spin the wheel?
[1]
An obstacle course has 1 Fences and 1 Ditches. You have a 90% chance of clearing a Fence and a 50% chance of clearing a Ditch.
What is the probability of having a perfect run (clearing everything)?
[1]
A group of humans did a math test and here are their scores out of 5:
humans

Score06
14
25
3
43
52

What fraction of the humans score exactly 4?
[2]
A wheel has 7 blue sections and 8 yellow sections.
What is the probability of getting blue?
[1]
There are 70 balls in a bag. This is is the probability distribution of their color:


0.20.40.4
orangegreenblue
Color

How many orange balls were in the bag?
[1]
Flip a coin 12 times.
Each time a head comes up you win $3 and with each tail you lose $4. It costs $13 to play (paid once). How much money would you expect to make altogether?
[1]
There are 90 balls in a bag. This is is the probability distribution of their color:


0.20.40.4
purpleredblue
Color

If you choose a random ball from the bag, what is the probability of it being purple or blue?
[1]
There are 20 balls in a bag. This is is the probability distribution of their color:


0.30.10.6
bluegreenyellow
Color

How many blue balls were in the bag?
[1]
Cars go by on a road, each is a different color and type.

Probability of Color

0.50.5
redyellow
Color

Probability of Type

0.10.9
wagonsedan
Type

What is the probability of a car being a red wagon?
[2]
A group of kids were timed running 100m. Here are the results:
kids

32465
1314151617
Time

What is the probability of the kids to run 100m in less than 13s?
[2]
A Crazy Die has 5 sides, but each side has a different probability of being rolled. This is is the probability distribution of the sides being rolled:


0.60.050.10.25
12345
Number

What is the probability of rolling a number that is bigger than 1?
[1]
A group of humans were timed running 100m. Here are the results:
humans

Time13
143
154
165
172

What fraction of the humans run 100m in exactly 17s?
[2]
A group of people did a math test and here are their scores out of 5:
people

113512
012345
Score

What fraction of the people score less than 2?
[2]
A bag has 4 balls with number 2 and 7 balls with a number 3. What will be the average of the numbers of the balls taken out of the bag
[1]