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?

  • A 1 6
  • B 5 6
  • C 2 3
  • D 1 2

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?

  • A 1 2 1 7
  • B 4 1 7
  • C 8 1 7
  • D 5 1 7
  • E 1 3 1 7

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.

  • A 3 8
  • B 5 8
  • C 5 9
  • D 1 2
  • E 1 4

Q4:

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

  • A 4 7
  • B 3 7
  • C 3 8
  • D 1 2
  • E 5 7

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.

  • A 1 3
  • B 3 7
  • C 1 2
  • D 2 3

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?

  • A 1 6
  • B 1 2
  • C 1 3
  • D0

Q8:

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

  • A0
  • B 1 2
  • C 1 6
  • D1

Q9:

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

  • A 3 8
  • B 1 4
  • C 1 2
  • D 9 1 6

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?

  • A 2 1 7
  • B 3 1 7
  • C 3 1 6
  • D 1 8
  • E 1 4

Q11:

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

  • A 7 1 7
  • B 4 1 7
  • C 6 1 7
  • D 1 3 1 7

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?

  • A 5 1 1
  • B 4 1 1
  • C 9 2 2
  • D 5 2 2

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?

  • A 2 9 6 0
  • B 8 1 5
  • C 7 1 5
  • D 1 1 2 0
  • E 1 6 3 5

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?

  • A 2 5 3 8
  • B 5 3 8
  • C 2 1 9
  • D 9 3 8
  • E 2 9 3 8

Q15:

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

  • A 1 8
  • B 1 2
  • C 1 4
  • D 3 8

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”?

  • A 1 3
  • B 2 5
  • C 1 5
  • 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?

  • A 1 1 3
  • B 1 2 6
  • C 1 5 2
  • D 1 2
  • E 1 4

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?

  • A 1 4
  • B 1 1 3
  • C 1 5 2
  • D 1 2 6
  • E 1 2

Q18:

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

  • A 1 2
  • B 5 6
  • C 2 3
  • D 1 3

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?

  • A 7 2 2
  • B 9 2 2
  • C 3 1 1
  • D 1 5 2 2

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?

  • A327
  • B339
  • C357
  • D346

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?

  • A 1 9 3 0
  • B 2 3
  • C 1 5
  • D 1 6

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?

  • A 9 1 1
  • B 7 1 1
  • C 2 1 1
  • D0
  • E1

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?

  • A 2 9 3 8
  • B 1 3 1 9
  • C 5 1 9
  • D 9 3 8
  • E 1 4 1 9

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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