simple
compound
permutations
challenge
100

Blank rolls a fair dice, with sides labeled A, B, C, D, E and F. What is the probability that the dice lands on a vowel?

1/6

100

What is the probability of getting heads three times in a row when flipping a coin three times?

1/8

100

Mateo is playing a word game where he's trying to make 4-letter words by rearranging the letters in the word IRON.   How many unique ways are there to arrange the letters in the word IRON?

24

100

12 people, forming 6 married couples, sit at a table. How many different seating arrangements can be made if each husband must sit immediately to the left of their wife?

720

200

On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?

1/3

200

Three coins are tossed up in the air, one at a time. What is the probability that two of them will land heads up and one will land tails up?

1/8

200

In how many different orders can 8 players sit on the basketball bench?

40,320

200

A fair coin is tossed three times. What is the probability of getting two heads and one tail (in any order)?

3/8

300

If you roll two fair six sided dice, what is the probability that the sum is 9 or higher?

5/18

300

A fair coin is flipped, and then a 6-sided die is rolled.
What is the probability of getting heads and then rolling a 4?

1/12

300

Amara needs to create a special tasting menu at her restaurant. She needs to select 4 dishes from 7 available dishes and put them in a tasty sequence. How many unique ways are there to arrange 4 of the 7 dishes?

840

300

There are 18 girls and 12 boys in a class. 2/9 of the girls and 1/4 of the boys walk to school. One of the students who walks to school is chosen at random. Find the probability that the student is a boy.  

3/7

400

Alice has some red and blue markers in a bag, 25 in total. Alice picks one marker from the bag. The probability that Alice picks a red marker is x and the probability that Alice picks a blue marker is 4x. How many blue markers are there?

20 blue markers

400

A bag contains 3 red, 2 blue, and 1 green marble. Two marbles are drawn without replacement.
What is the probability of drawing a red marble both times?

1/5

400

Ms. Miranda writes the names of 6 songs on the board, and then plays 4 songs out of the 6, one after the other in a random sequence. Diya then needs to identify each of the songs in the sequence they were played. Suppose that Diya is randomly guessing the songs. What is the probability that she correctly identifies all 4 songs in the correct order?

1/360

400

How many possible distinct arrangements are there of the letters in the word BALL?

12

500

 A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7?

13/90

500

3 people were chosen at random. Find the theoretical probability that all 3 were born on the same weekday?

1/343

500

You have 9 different books, but 3 of them are a trilogy that must stay together in order.
How many different ways can you arrange all 9 books on a shelf?

5040

500

Sam asked 50 people whether they like vegetable pizza or pepperoni pizza. 37 people like vegetable pizza. 25 people like both. 3 people like neither. Sam picked one of the 50 people at random. Given that the person he chose likes pepperoni pizza, find the probability that they don’t like vegetable pizza. 

2/7

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