# Worksheet: Theoretical Probability

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

**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
- B
- C
- D
- E

**Q7: **

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

- A
- B
- C
- D0

**Q8: **

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

- A0
- B
- C
- D1

**Q9: **

A number is chosen at random from the set . What is the probability that the number is even?

- A
- B
- C
- D

**Q10: **

Two distinct digits are chosen at random from the set . What is the probability that the sum of the two digits is 13?

- A
- B
- C
- D
- E

**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
- B
- C
- D

**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
- B
- C
- D

**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
- B
- C
- D
- E

**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
- B
- C
- D
- E

**Q15: **

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

- A
- B
- C
- D

**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
- B
- C
- 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
- B
- C
- D
- E

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
- B
- C
- D
- E

**Q18: **

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

- A
- B
- C
- D

**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
- B
- C
- D

**Q20: **

A bag contains white, red, and black balls. The probability of drawing a white ball at random is and a red ball at random is . 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?

- A
- B
- C
- D

**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?

- A
- B
- C
- D
- E

**Q25: **

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