Probability Powerplay
Level 6, 2025-09-17
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:


0.90.050.05
12345
Number

What is the probability of rolling a number that is smaller than 3?
[1]
Flip a coin 6 times.
How many times would you expect to get Tails?
[1]
We asked a group of people how many Burgers they eat in a day. Here are the results:
people

Burgers03
13
25
32

What fraction of the people eat exactly 3 Burgers in a day?
[2]
Flip a coin 6 times.
Each time a head comes up you win $2 and with each tail you lose $4. How much money would you expect to make altogether?
[1]
Roll 114 6-sided dice.
How many times would you expect to get anything except 2?
[1]
A group of boys did a math test and here are their scores out of 5:
boys

Score03
15
24
35
4
52

What is the probability of the boys to score exactly 2?
[2]
A group of boys did a math test and here are their scores out of 5:
boys

Score03
12
25
34
44
56

What is the probability of the boys to score more than 3?
[2]
A wheel has 8 sections, each a number on it from 1 to 8. If you spin an even number you win that amount of dollars, if you spin an odd number you lose.
What prize do we expect to get if we spin the wheel?
[1]
Roll 54 6-sided dice.
How many times would you expect to get less than 1?
[1]
Roll a die 120 times.
How many times would you expect to get a 1?
[1]
Flip a coin 10 times.
Each time a head comes up you win $4 and with each tail you lose $1. It costs $8 to play (paid once). How much money would you expect to make altogether?
[1]
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:


0.450.150.150.150.1
12345
Number

What is the probability of rolling a number from 4 to 5?
[1]
You shoot an arrow at a target. There is a 50% chance of scoring a 10, a 40% chance of scoring a 40, or you might miss completely and score 0. What average score do you expect to get if you do this many times?
[1]
Flip a coin 2 times.
Each time a head comes up you win $3 and with each tail you lose $1. How much money would you expect to make altogether?
[1]
We asked a group of boys how many Pizzas they eat in a month. Here are the results:
boys

62
0123
Pizzas

What fraction of the boys eat more than 3 Pizzas in a month?
[2]
Flip a coin 6 times.
Each time a head comes up you win $1 and with each tail you lose $1. How much money would you expect to make altogether?
[1]