Worksheet: Theoretical Probability

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

Q1:

What it is the probability of rolling a number greater than or equal to 2 on a regular dice?

  • A16
  • B56
  • C23
  • D12

Q2:

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

Q3:

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

Q4:

If this spinner is spun once, what is the probability of NOT getting a vowel? Give your answer as a fraction.

  • A47
  • B37
  • C38
  • D12
  • E57

Q5:

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

  • A13
  • B37
  • C12
  • D23

Q6:

When spinning a fair coin, what is the probability that it lands heads side up?

Q7:

What is the probability of rolling a number between 0 and 2 on a fair die?

  • A16
  • B12
  • C13
  • D0

Q8:

What it is the probability of rolling a number less than or equal to 1 on a regular dice?

  • A0
  • B12
  • C16
  • D1

Q9:

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

Q10:

Two distinct digits are chosen at random from the set {2,4,5,8}. What is the probability that the sum of the two digits is 13?

  • A217
  • B317
  • C316
  • D18
  • E14

Q11:

A box contains 7 white, 4 black, and 6 red balls. What is the probability of drawing a black ball from the box?

  • A717
  • B417
  • C617
  • D1317

Q12:

A bag contains 5 yellow balls, 9 white balls, and 8 red balls. If a ball is chosen at random from the bag, what is the probability that it is white?

  • A511
  • B411
  • C922
  • D522

Q13:

A class of 60 students contains 32 boys and 28 girls. If a student is picked at random, what is the probability that the student is a girl?

  • A2960
  • B815
  • C715
  • D1120
  • E1635

Q14:

A school club has 25 boys and 13 girls. Of the members in the club 5 of the boys and 4 of the girls wear glasses. If a club member is chosen at random, what is the probability that they do not wear glasses?

  • A2538
  • B538
  • C219
  • D938
  • E2938

Q15:

Determine the probability that the given fair spinner will stop on a green section when spun.

  • A18
  • B12
  • C14
  • D38

Q16:

The letters of the word “Sohag” are written on different cards and placed in a box. What is the probability of selecting at random the card with the letter “Y”?

  • A13
  • B25
  • C15
  • D0

Q17:

A magician asked a spectator to choose a card from a standard deck of playing cards. The spectator took a card, looked at it, and then put it back into the deck in a different position. The spectator, however, did not know that the magician had arranged the pack so that every black card had a red card on either side of it.

What is the probability that the magician would correctly identify the card?

  • A113
  • B126
  • C152
  • D12
  • E14

If the magician asked the spectator to reveal the color of the card they had chosen, what would the new probability of the magician correctly identifying the card be?

  • A14
  • B113
  • C152
  • D126
  • E12

Q18:

What is the probability of rolling a number between 3 and 7 on a fair die?

  • A12
  • B56
  • C23
  • D13

Q19:

A bag contains 7 red sweets, 6 black sweets, and 9 green sweets. If a sweet is drawn randomly from the bag, what is the probability of drawing a red sweet?

  • A722
  • B922
  • C311
  • D1522

Q20:

A bag contains white, red, and black balls. The probability of drawing a white ball at random is 1120 and a red ball at random is 310. How many red balls and how many black balls are in the bag?

  • A5, 4
  • B11, 3
  • C6, 3
  • D3, 6
  • E11, 6

Q21:

What is the expected number of tails when a fair coin is flipped 690 times?

Q22:

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

Q23:

A bag contains 9 white balls and 2 red balls. If a ball is chosen at random from the bag, what is the probability that the ball is white or red?

Q24:

A class in a school contains 38 students. At the end of the school year 29 of the students passed mathematics, 28 passed science, and 26 passed both science and mathematics. If a student is chosen at random from the class, what is the probability that they passed in science?

  • A2938
  • B1319
  • C519
  • D938
  • E1419

Q25:

At a school fair 68 people entered a raffle. Given that the probability of a girl winning the raffle is 14, and people can only enter once, how many girls took part in the raffle?

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