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Lesson Worksheet: Theoretical Probability Mathematics

In this worksheet, we will practice interpreting a data set by finding and evaluating the theoretical probabilities.


A box contains 5 red marbles, 8 green marbles, and 4 yellow marbles. If a marble is picked from the box at random, what is the probability that the marble is red?

  • A1217
  • B417
  • C817
  • D517
  • E1317


If this spinner is spun once, what is the probability of getting a vowel? Give your answer as a fraction in its simplest form.

  • A38
  • B58
  • C59
  • D12
  • E14


A number is chosen at random from the set {3,4,7,8}. What is the probability that the number is even?

  • A38
  • B14
  • C12
  • D916


What is the probability of rolling a number greater than or equal to 4 on a fair die?

  • A23
  • B0
  • C12
  • D13


A bag contains an unknown number of balls. Given that one-sixth of the balls are white, one-fifth of them are green, and the rest are blue, what is the probability that a ball drawn at random from the bag is blue?

  • A1930
  • B23
  • C15
  • D16


A bag contains 30 colored marbles. The probability of choosing a white marble at random is 25. How many white marbles are in the bag?


In a class of 50 students, 33 passed the mathematics test and 31 passed the language test. What is the probability that a randomly selected student failed in the language test?

  • A3350
  • B1950
  • C1750
  • D3150


A class contains 59 students. In the class, the number of boys exceeds the number of girls by 7. If a student is chosen at random, what is the probability the student is a boy?

  • A2659
  • B3459
  • C3359
  • D3259


A bag contains 7 pennies, 10 nickels, and 7 dimes. How many coins of each type should be added to increase the number of coins to 48, while keeping the probability of randomly selecting each type of coin the same?

  • A8 pennies, 10 nickels, and 8 dimes
  • B7 pennies, 7 nickels, and 7 dimes
  • C9 pennies, 11 nickels, and 8 dimes
  • D7 pennies, 7 nickels, and 10 dimes
  • E7 pennies, 10 nickels, and 7 dimes


A card is selected at random from a pack of 52 cards which are numbered 1 to 52. What is the probability that the selected card has a number which is neither a perfect square nor a multiple of 6?

  • A34
  • B3752
  • C1926
  • D4552
  • E3552

This lesson includes 47 additional questions and 474 additional question variations for subscribers.

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